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Yoichi Arai, Taisuke Otsu and Myung Hwan Seo

This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate sele...Read more...

31 October 2022

Yoichi Arai, Taisuke Otsu and Mengshan Xu

The generalized least square (GLS) is one of the most basic tools in regression analyses. A major issue in implementing the GLS is estimation of the conditional variance function of the error term, which typically requir...Read more...

27 October 2022

Sreevidya Ayyar, Yukitoshi Matsushita and Taisuke Otsu

This paper extends validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003) to instrumental variable regression models with unknown error variance and many weak instruments. In this setting, we...Read more...

11 October 2022

Taisuke Otsu and Mengshan Xu

We propose a one-to-many matching estimator of the average treatment effect based on propensity scores estimated by isotonic regression. The method relies on the monotonicity assumption on the propensity score function, ...Read more...

19 July 2022

Javier Hidalgo, Heejun Lee, Heejun Lee, Jungyoon Lee and Myung Hwan Seo

We derive a risk lower bound in estimating the threshold parameter without knowing whether the threshold regression model is continuous or not. The bound goes to zero as the sample size n grows only at the cube root ra...Read more...

3 March 2022

Abhimanyu Gupta and Javier Hidalgo

We describe a (nonparametric) prediction algorithm for spatial data, based on a canonical factorization of the spectral density function. We provide theoretical results showing that the predictor has desirable asymptot...Read more...

Hao Dong, Taisuke Otsu and Luke Taylor

We propose two novel bandwidth selection procedures for the nonparametric regression model with classical measurement error in the regressors. Each method is based on evaluating the prediction errors of the regression us...Read more...

25 January 2022

Yukitoshi Matsushita, Taisuke Otsu and Keisuke Takahata

In various fields of data science, researchers often face problems of estimating the ratios of two probability densities. Particularly in the context of causal inference, the product of marginals for a treatment variable...Read more...

7 January 2022

Taisuke Otsu and Martin Pesendorfer

This paper surveys the recent literature on dynamic games estimation when there is a concern of equilibrium multiplicity. We focus on the questions of testing for equilibrium multiplicity and estimation in the presence o...Read more...

26 October 2021

Harold D Chiang, Yukitoshi Matsushita and Taisuke Otsu

his paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. We propose a novel multiway empirical likeli- hood statistic that converges to a chi-square...Read more...

19 October 2021

Daisuke Kurisu and Taisuke Otsu

This paper studies asymptotic properties of the local linear quantile estimator under the extremal order quantile asymptotics, and develops a practical inference method for conditional quantiles in extreme tail areas. By...Read more...

14 September 2021

By utilizing intermediate Gaussian approximations, this paper establishes asymptotic linear representations of nonparametric deconvolution estimators for the classical measurement error model with repeated measurements. ...Read more...

19 July 2021

Karun Adusumilli, Taisuke Otsu and Chen Qiu

This paper is concerned with inference on finite dimensional parameters in semiparametric moment condition models, where the moment functionals are linear with respect to unknown nuisance functions. By exploiting this li...Read more...

1 December 2020

Yukitoshi Matsushita and Taisuke Otsu

This paper proposes a jackknife Lagrange multiplier (JLM) test for instrumental variable regression models, which is robust to (i) many instruments, where the number of instruments may increase proportionally with the sa...Read more...

5 August 2020

This paper studies second-order properties of the many instruments robust t-ratios based on the limited information maximum likelihood and Fuller estimators for instrumental variable regression models under the many inst...Read more...

12 May 2020

Taisuke Otsu, Martin Pesendorfer, Yuya Sasaki and Yuya Takahashi

We propose a multiplicity-robust estimation method for (static or dynamic) games. The method allows for distinct behaviors and strategies across markets by treating market specific behaviors as correlated latent variable...Read more...

20 January 2020

V A Hajivassiliou

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8 January 2020

This paper proposes efficient estimation methods for panel data limited dependent variables (LDV) models possessing a variety of complications: non-ignorable persistent heterogeneity; contemporaneous and intertemporal en...Read more...

3 December 2019

Hidehiko Ichimura, Taisuke Otsu and Joseph Altonji

This paper studies nonparametric estimation of d-dimensional conditional quantile functions and their derivatives in the tails. We investigate asymptotic properties of the local and global nonparametric quantile regressi...Read more...

26 November 2019

We propose a semiparametric estimator for varying coeﬃcient models when the regressors in the nonparametric component are measured with error. Varying coeﬃcient models are an extension of other popular semi...Read more...

V A Hajivassiliou, Frédérique Savignac and Frédérique Savignac

We develop novel methods for establishing coherency conditions in Static and Dynamic Limited Dependent Variables (LDV) Models. We propose estimation strategies based on Conditional Maximum Likelihood Estimation for simul...Read more...

5 November 2019

This paper sheds light on problems of statistical inference under alternative or nonstandard asymptotic frameworks from the perspective of jackknife empirical likelihood (JEL). Examples include small bandwidth asymptotic...Read more...

22 July 2019

This paper studies the uniform convergence rates of Li and Vuong's (1998) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015) for the classical measurement error model, where repe...Read more...

Mengshan Xu and Taisuke Otsu

17 May 2019

7 January 2019

Hao Dong and Taisuke Otsu

In estimation of nonparametric additive models, conventional methods, such as backfitting and series approximation, cannot be applied when measurement errors are present in covariates. We propose an estimator for such ...Read more...

27 November 2018

Karun Adusumilli and Taisuke Otsu

Missing or incomplete outcome data is a ubiquitous problem in biomedical and social sciences. Under the missing at random setup, inverse probability weighting is widely applied to estimate and make inference on the popul...Read more...

30 October 2018

Koen Jochmans and Taisuke Otsu

The use of two-way fixed-effect models is widespread. The presence of incidental parameter bias, however, invalidates statistical inference based on the likelihood. In this paper we consider modifications to the (profile...Read more...

19 February 2018

Javier Hidalgo and Marcia M Schafgans

This paper addresses inference in large panel data models in the presence of both cross-sectional and temporal dependence of unknown form. We are interested in making inferences without relying on the choice of any smoo...Read more...

20 February 2018

Jungyoon Lee and Peter M Robinson

We consider adaptive tests and estimates which are asymptotically efficient in the presence of unknown, nonparametric, distributional form in pure spatial models. A novel adaptive Lagrange Multiplier testing procedure f...Read more...

26 January 2018

Taisuke Otsu and Chen Qiu

This paper is concerned with estimation of functionals of a latent weight function that satisfies possibly high dimensional multiplicative moment conditions. Main examples are missing data problems, treatment effects, an...Read more...

4 January 2018

Karun Adusumilli, Taisuke Otsu and Yoon-Jae Whang

13 November 2017

Lorenzo Camponovo, Yukitoshi Matsushita and Taisuke Otsu

This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties for the approximation of tail area probabilities. Our statistic, called the tilted ex...Read more...

In the past few decades, much progress has been made in semiparametric modeling and estimation methods for econometric analysis. This paper is concerned with inference (i.e., confidence intervals and hypothesis testing) ...Read more...

27 June 2017

With increasing availability of high frequency financial data as a background, various volatility measures and related statistical theory are developed in the recent literature. This paper introduces the method of empiri...Read more...

21 February 2017

Javier Hidalgo, Jungyoon Lee and Myung Hwan Seo

This paper is concerned with inference in regression models with either a kink or a jump at an unknown threshold, particularly when we do not know whether the kink or jump is the true specification. One of our main resu...Read more...

13 February 2017

Myung Hwan Seo and Taisuke Otsu

This paper examines asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, conditional maximum scor...Read more...

17 October 2016

Hahn and Ridder (2013) formulated influence functions of semiparametric three step estimators where generated regressors are computed in the first step. This class of estimators covers several important examples for empi...Read more...

5 September 2016

Taisuke Otsu and Luke Taylor

This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniqu...Read more...

15 August 2016

This paper considers nonparametric instrumental variable regression when the endogenous variable is contaminated with classical measurement error. Existing methods are inconsistent in the presence of measurement error. W...Read more...

21 July 2015

Violetta Dalla and Javier Hidalgo

4 June 2015

This paper is concerned with various issues related to inference in large dynamic panel data models (where both n and T increase without bound) in the presence of, possibly, strong cross-sectional dependence. Our first a...Read more...

1 April 2015

Taisuke Otsu, Martin Pesendorfer and Yuya Takahashi

This paper proposes several statistical tests for finite state Markov games to examine the null hypothesis that data from distinct markets can be pooled. We formulate tests of (i) the conditional choice and state transit...Read more...

16 March 2015

We propose a nonparametric likelihood inference method for the integrated volatility under high frequency financial data. The nonparametric likelihood statistic, which contains the conventional statistics such as empiric...Read more...

15 January 2015

Taisuke Otsu and Yoshiyasu Rai

Abadie and Imbens (2008) showed that the standard naive bootstrap is inconsistent to estimate the distribution of the matching estimator for treatment effects with a fixed number of matches. This article proposes an asym...Read more...

13 January 2015

Kirill Evdokimov, Yuichi Kitamura and Taisuke Otsu

This paper considers robust estimation of moment condition models with time series data. Researchers frequently use moment condition models in dynamic econometric analysis. These models are particularly useful when one w...Read more...

5 December 2014

Clifford Lam and Pedro Souza

This paper proposes a model for estimating the underlying cross-sectional dependence structure of a large panel of time series. Technical difficulties meant such a structure is usually assumed before further analysis. We...Read more...

25 November 2014

Myung Hwan Seo and Yongcheol Shin

This paper addresses an important and challenging issue as how best to model nonlinear asymmetric dynamics and cross-sectional heterogeneity, simultaneously, in the dynamic threshold panel data framework, in which both t...Read more...

1 September 2014

Javier Hidalgo and Jungyoon Lee

This paper examines a nonparametric CUSUM-type test for common trends in large panel data sets with individual fixed effects. We consider, as in Zhang, Su and Phillips (2012), a partial linear regression model with unkno...Read more...

In this paper we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to b...Read more...

6 August 2014

We extend the method of empirical likelihood to cover hypotheses involving the Aumann expectation of random sets. By exploiting the properties of random sets, we convert the testing problem into one involving a continuum...Read more...

25 June 2014

Taisuke Otsu, Ke-Li Xu and Yukitoshi Matsushita

7 February 2014

Lorenzo Camponovo and Taisuke Otsu

This paper studies robustness of bootstrap inference methods for instrumental variable (IV)regression models. We consider test statistics for parameter hypotheses based on the IV estimatorand generalized method of trimme...Read more...

21 January 2014

Abstract. Since Manski's (1975) seminal work, the maximum score method for discrete choice models has been applied to various econometric problems. Kim and Pollard (1990) established the cube root asymptotics for the max...Read more...

Revised August 2014

An asymptotic theory is developed for nonparametric and semiparametric series estimation under general cross-sectional dependence and heterogeneity. A uniform rate of consistency, asymptotic normality, and sufficient con...Read more...

25 November 2013

Nonparametric regression is developed for data with both a temporal and a cross-sectional dimension. The model includes additive, unknown, individual-specifi…c components and allows also for cross-sectional and temporal ...Read more...

Miguel A. Delgado and Peter M Robinson

We develop non-nested tests in a general spatial, spatio-temporal or panel data context. The spatial aspect can be interpreted quite generally, in either a geographical sense, or employing notions of economic distance, o...Read more...

Peter M Robinson and Carlos Velasco

A dynamic panel data model is considered that contains possibly stochastic individual components and a common fractional stochastic time trend. We propose four different ways of coping with the individual effects so as t...Read more...

20 November 2013

Peter M Robinson and Francesca Rossi

For testing lack of correlation against spatial autoregressive alternatives, Lagrange multiplier tests enjoy their usual computational advantages, but the (x squared) first-order asymptotic approximation to critical valu...Read more...

We consider testing the null hypothesis of no spatial autocorrelation against the alternative of first order spatial autoregression. A Wald test statistic has good first order asymptotic properties, but these may not be ...Read more...

Tatiana Komarova

The paper considers nonparametric estimation of absolutely continuous distribution functions of lifetimes of non-identical components in k-out-of-n systems from the observed “autopsy” data. In economics,ascending “button...Read more...

27 August 2013

Javier Hidalgo, Pedro Souza and Pedro Souza

Nowadays it is very frequent that a practitioner faces the problem of modelling large data sets. Relevant examples include spatio-temporal or panel data models with large N and T. In these cases deciding a particular dyn...Read more...

1 July 2013

Javier Hidalgo and Myung Hwan Seo

We consider an omnibus test for the correct speci…cation of the dynamics of a sequence fx (t)gt2Zd in a lattice. As it happens with causal models and d = 1, its asymptotic distribution is not pivotal and depends on the e...Read more...

15 May 2013

The paper examines a Lagrange Multiplier type test for the constancy of the parameter in general models with dependent data without imposing any arti…cial choice of the possible location of the break. In order to prove t...Read more...

1 September 2012

This paper revisits testability of complementarity in economic models with multiple equilibria studied by Echenique and Komunjer (2009). We find that Echenique and Komunjer’s (2009) testable implications on extreme quant...Read more...

1 February 2013

In semiparametric binary response models, support conditions on the regressors are required to guarantee point identification of the parameter of interest. For example,one regressor is usually assumed to have continuous ...Read more...

1 May 2012

Javier Hidalgo and Myunghwan Seo

The paper examines a Lagrange Multiplier type test for the constancy of the parameter in general models with dependent data without imposing any artificial choice of the possible location of the break. In order to prove ...Read more...

1 October 2011

Yulia Kotlyarova, Marcia M Schafgans and Victoria Zinde-Walsh

For local and average kernel based estimators, smoothness conditions ensure that the kernel order determines the rate at which the bias of the estimator goes to zero and thus allows the econometrician to control the rate...Read more...

April 2011

Peter M Robinson

Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space-time. Consistency and asymptotic...Read more...

May 2011

Nonparametric regression with spatial, or spatio-temporal, data is considered. The conditional mean of a dependent variable, given explanatory ones, is a nonparametric function, while the conditional covariance reflects ...Read more...

September 2010

Peter M Robinson and Supachoke Thawornkaiwong

Central limit theorems are developed for instrumental variables estimates of linear and semi-parametric partly linear regression models for spatial data. General forms of spatial dependence and heterogeneity in explanato...Read more...

April 2010

Panel data, whose series length T is large but whose cross-section size N need not be, are assumed to have a common time trend. The time trend is of unknown form, the model includes additive, unknown, individual-specific...Read more...

January 2010

Tatiana Komarova, Thomas Severini and Elie Tamer

We introduce a notion of median uncorrelation that is a natural extension of mean (linear) uncorrelation. A scalar random variable Y is median uncorrelated with a kdimensional random vector X if and only if the slope fro...Read more...

Bonsoo Koo and Oliver Linton

This paper proposes a class of locally stationary diffusion processes. The model has a time varying but locally linear drift and a volatility coefficient that is allowed to vary over time and space. We propose estimators...Read more...

August 2010

Sorawoot Srisuma and Oliver Linton

We propose a general two-step estimation method for the structural parameters of popular semiparametric Markovian discrete choice models that include a class of Markovian Games and allow for continuous observable state s...Read more...

Degui Li, Zudi Lu and Oliver Linton

Local linear fitting is a popular nonparametric method in nonlinear statistical and econometric modelling. Lu and Linton (2007) established the point wise asymptotic distribution (central limit theorem) for the local lin...Read more...

Sorawoot Srisuma

Bajari, Benkard and Levin (2007) propose an estimation methodology for a broad class of dynamic optimization problems. To carry out their procedure, one needs to select a set of alternative policy functions and compare t...Read more...

May 2010

This paper proposes an approach to proving nonparametric identification for distributions of bidders' values in asymmetric second-price auctions. I consider the case when bidders have independent private values and the o...Read more...

October 2009

Christian M. Hafner and Oliver Linton

We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel (2008), which has a nonparametric long run component and a unit multivariate GARCH short run dynamic component. We sugge...Read more...

Woocheol Kim and Oliver Linton

We propose a semiparametric IGARCH model that allows for persistence in variance but also allows for more flexible functional form. We assume that the difference of the squared process is weakly stationary. We propose an...Read more...

Oliver Linton, Søren Feodor Nielsen and Jens Perch Nielsen

In this paper we investigate a class of semiparametric models for panel datasets where the cross-section and time dimensions are large. Our model contains a latent time series that is to be estimated and perhaps forecast...Read more...

Wolfgang Härdle, Oliver Linton and Yingcun Xia

In semiparametric models it is a common approach to under-smooth the nonparametric functions in order that estimators of the finite dimensional parameters can achieve root-n consistency. The requirement of under-smoothin...Read more...

July 2009

Xiaohong Chen, David T. Jacho-Chávez and Oliver Linton

A new way of constructing efficient semiparametric instrumental variable estimators is proposed. The method involves the combination of a large number of possibly inefficient estimators rather than combining the instrume...Read more...

June 2009

Efang Kong, Oliver Linton and Yingcun Xia

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Y_i,?X_i ) } . We establish a strong uniform consistency rate for the Bahadur representation ...Read more...

January 2009

Gordon Anderson, Oliver Linton and Yoon-Jae Whang

This paper develops methodology for nonparametric estimation of a polarization measure due to Anderson (2004) and Anderson, Ge, and Leo (2006) based on kernel estimation techniques. We give the asymptotic distribution th...Read more...

We consider cross-sectional data that exhibit no spatial correla- tion, but are feared to be spatially dependent. We demonstrate that a spatial version of the stochastic volatility model of financial econometrics, entail...Read more...

The central limit theorem for nonparametric kernel estimates of a smooth trend, with linearly-generated errors, indicates asymptotic independence and homoscedasticity across fixed points, irrespective of whether disturba...Read more...

Disregarding spatial dependence can invalidate methods for analyzing cross-sectional and panel data. We discuss ongoing work on developing methods that allow for, test for, or estimate, spatial dependence. Much of the st...Read more...

We provide a general class of tests for correlation in time series, spatial, spatiotemporal and cross-sectional data. We motivate our focus by reviewing how computational and theoretical difficulties of point estimation ...Read more...

Marcia M Schafgans and Victoria Zinde-Walsh

Many important models, such as index models widely used in limited dependent variables, partial linear models and nonparametric demand studies utilize estimation of average derivatives (sometimes weighted) of the conditi...Read more...

August 2008

Oliver Linton, Kyungchul Song and Yoon-Jae Whang

We propose a new method of testing stochastic dominance which improves on existing tests based on bootstrap or subsampling. Our test requires estimation of the contact sets between the marginal distributions. Our tests h...Read more...

February 2008

Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter (?), at the frequency of principal interest, zero; for short memory series ? = 0 automatically. The latter case h...Read more...

October 2007

Gregory Connor, Matthias Hagmann and Oliver Linton

This paper develops a new estimation procedure for characteristic-based factor models of security returns. We treat the factor model as a weighted additive nonparametric regression model, with the factor returns serving ...Read more...

Ilze Kalnina and Oliver Linton

We investigate the use of subsampling for conducting inference about the quadratic variation of a discretely observed diffusion process under an infill asymptotic scheme. We show that the usual subsampling method of Poli...Read more...

September 2007

Peter Robinson

We develop a sequence of tests for specifying the cointegrating rank of, possibly fractional, multiple time series. Memory parameters of observables are treated as unknown, as are those of possible cointegrating errors. ...Read more...

We consider a multivariate continuous time process, generated by a system of linear stochastic differential equations, driven by white noise and involving coefficients that possibly vary over time. The process is observa...Read more...

June 2007

Afonso Gonçalves da Silva and Peter M Robinson

Asset returns are frequently assumed to be determined by one or more common factors. We consider a bivariate factor model, where the unobservable common factor and idiosyncratic errors are stationary and serially uncorre...Read more...

May 2007

Javier Hidalgo

We describe and examine a consistent test for the correct specification of a regression function with dependent data. The test is based on the supremum of the difference between the parametric and nonparametric estimates...Read more...

Myung Hwan Seo

Asymptotic inference in nonlinear vector error correction models (VECM) that exhibit regime-specific short-run dynamics is nonstandard and complicated. This paper contributes the literature in several important ways. Fir...Read more...

March 2007

Sokbae Lee and Myunghwan Seo

This paper is concerned with semiparametric estimation of a threshold binary response model. The estimation method considered in the paper is semiparametric since the parameters for a regression function are finite-dimen...Read more...

February 2007

Efficient semiparametric and parametric estimates are developed for a spatial autoregressive model, containing nonstochastic explanatory variables and innovations suspected to be non-normal. The main stress is on the cas...Read more...

Marcia M Schafgans and Morton Stelcnery

In this paper we revisit the gender decomposition of wages in the presence of selection bias. We show that when labor market participation decisions of couples are not independent, the sample selection corrections used i...Read more...

December 2006

We propose an econometric model that captures the e¤ects of market microstructure on a latent price process. In particular, we allow for correlation between the measurement error and the return process and we allow the m...Read more...

October 2006

David T. Jacho-Chávez, Arthur Lewbel and Oliver Linton

Let r (x, z) be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses identification and consistent estimation of the unknown functions H, M, G and F, where r ...Read more...

September 2006

Arthur Lewbel, Oliver Linton and DL McFadden

A statistical problem that arises in several fields is that of estimating the features of an unknown distribution, which may be conditioned on covariates, using a sample of binomial observations on whether draws from thi...Read more...

Gregory Connor and Oliver Linton

We introduce an alternative version of the Fama-French three-factor model of stock returns together with a new estimation methodology. We assume that the factor betas in the model are smooth nonlinear functions of observ...Read more...

Employing recent results of Robinson (2005) we consider the asymptotic properties of conditional-sum-of-squares (CSS) estimates of parametric models for stationary time series with long memory. CSS estimation has been co...Read more...

Sokbae Lee, Oliver Linton and Yoon-Jae Whang

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution i...Read more...

August 2006

Oliver Linton and Enno Mammen

We consider a semiparametric distributed lag model in which the “news impact curve” m is nonparametric but the response is dynamic through some linear filters. A special case of this is a nonparametric regression with se...Read more...

Javier Hualde and Peter M Robinson

A semiparametric bivariate fractionally cointegrated system is considered, integration orders possibly being unknown and I (0) unobservable inputs having nonparametric spectral density. Two kinds of estimate of the coint...Read more...

May 2006

Nonlinear functions of multivariate financial time series can exhibit long memory and fractional cointegration. However, tools for analysing these phenomena have principally been justified under assumptions that are inva...Read more...

April 2006

Peter M Robinson and M. Gerolimetto

Instrumental variables estimation is classically employed to avoid simultaneous equations bias in a stable environment. Here we use it to improve upon ordinary least squares estimation of cointegrating regressions betwee...Read more...

Empirical evidence has emerged of the possibility of fractional cointegration such that the gap, ß, between the integration order d of observable time series, and the integration order ? of cointegrating errors, is less ...Read more...

March 2006

Smoothed nonparametric kernel spectral density estimates are considered for stationary data observed on a d-dimensional lattice. The implications for edge effect bias of the choice of kernel and bandwidth are considered....Read more...

February 2006

Violetta Dalla, Liudas Giraitis and Javier Hidalgo

For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties are well established. However, excep...Read more...

January 2006

Myunghwan Seo and Oliver Linton

We propose a smoothed least squares estimator of the parameters of a threshold regression model. Our model generalizes that considered in Hansen (2000) to allow the thresholding to depend on a linear index of observed re...Read more...

October 2005

Peter M Robinson and Paolo Zaffaroni

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH(8) processes are established. We require the ARCH weights to decay at least hyperbo...Read more...

Bas Donkers and Marcia M Schafgans

We propose an easy to use derivative based two-step estimation procedure for semi-parametric index models. In the first step various functionals involving the derivatives of the unknown function are estimated using nonpa...Read more...

July 2005

Peter M Robinson and J Vidal Sanz

In the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d >= 2, the achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more gene...Read more...

June 2005

Much time series data are recorded on economic and financial variables. Statistical modelling of such data is now very well developed, and has applications in forecasting. We review a variety of statistical models from t...Read more...

March 2005

The paper proposes a simple test for the hypothesis of strong cycles and as a by-product a test for weak dependence for linear processes. We show that the limit distribution of the test is the maximum of a (semi)Gaussian...Read more...

February 2005

Andrew J. Patton and Allan Timmermann

Evaluation of forecast optimality in economics and finance has almost exclusively been conducted on the assumption of mean squared error loss under which forecasts should be unbiased and forecast errors serially uncorrel...Read more...

January 2005

Myunghwan Seo

There is a growing literature on unit root testing in threshold autoregressive models. This paper makes two contributions to the literature. First, an asymptotic theory is developed for unit root testing in a threshold a...Read more...

Yoshihiko Nishiyama and Peter M Robinson

In a number of semiparametric models, smoothing seems necessary in order to obtain estimates of the parametric component which are asymptotically normal and converge at parametric rate. However, smoothing can inflate the...Read more...

Miguel A. Delgado, Javier Hidalgo and Carlos Velasco

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals...Read more...

We consider the estimation of the location of the pole and memory parameter, ?<sup>0</sup> and a respectively, of covariance stationary linear processes whose spectral density function f(?) satisfies f(?) ~ C|? - ?<sup>0...Read more...

We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and additive deterministic component cons...Read more...

November 2004

Trino-Manuel Niguez and Javier Perote

In this paper we introduce a transformation of the Edgeworth-Sargan series expansion of the Gaussian distribution, that we call Positive Edgeworth-Sargan (PES). The main advantage of this new density is that it is well d...Read more...

October 2004

Fabrizio Iacone and Peter M Robinson

We consider a cointegrated system generated by processes that may be fractionally integrated, and by additive polynomial and generalized polynomial trends. In view of the consequent competition between stochastic and det...Read more...

May 2004

Oliver Linton

This paper is concerned with the practical problem of conducting inference in a vector time series setting when the data is unbalanced or incomplete. In this case, one can work only with the common sample, to which a sta...Read more...

April 2004

Smoothed nonparametric estimates of the spectral density matrix at zero frequency have been widely used in econometric inference, because they can consistently estimate the covariance matrix of a partial sum of a possibl...Read more...

March 2004

Asymptotic inference on nonstationary fractional time series models, including cointegrated ones, is proceeding along two routes, determined by alternative definitions of nonstationary processes. We derive bounds for the...Read more...

Oliver Linton, Esfandiar Maasoumi and Yoon-Jae Whang

We propose a procedure for estimating the critical values of the extended Kolmogorov-Smirnov tests of Stochastic Dominance of arbitrary order in the general K-prospect case. We allow for the observations to be serially d...Read more...

December 2003

Oliver Linton and Yoon-Jae Whang

In this note we propose a simple method of measuring directional predictability and testing for the hypothesis that a given time series has no directional predictability. The test is based on the correlogram of quantile ...Read more...

November 2003

This paper examines a nonparametric test for Granger-causality for a vector covariance stationary linear process under, possibly, the presence of long-range dependence. We show that the test converges to a non-distributi...Read more...

Arthur Lewbel and Oliver Linton

For vectors x and w, let r(x,w) be a function that can be nonparametrically estimated consistently and asymptotically normally. We provide consistent, asymptotically normal estimators for the functions g and h, where r(x...Read more...

October 2003

Liudas Giraitis, Remigijus Leipus, Peter M Robinson and Donatas Surgailis

We consider the long memory and leverage properties of a model for the conditional variance of an observable stationary sequence, where the conditional variance is the square of an inhomogeneous linear combination of pas...Read more...

We investigate a new separable nonparametric model for time series, which includes many ARCH models and AR models already discussed in the literature. We also propose a new estimation procedure based on a localization of...Read more...

May 2003

Oliver Linton and Mototsugu Shintani

This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We intro...Read more...

Wolfgang Haerdle, Oliver Linton and Qihua Wang

We develop inference tools in a semiparametric regression model with missing response data. A semiparametric regression imputation estimator, a marginal average estimator and a (marginal) propensity score weighted estima...Read more...

We investigate a class of semiparametric ARCH(8) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible f...Read more...

The purpose of this paper is to introduce and examine two alternative, although similar, approaches to the Moving Blocks and subsampling Bootstraps to bootstrapping the estimator of the parameters for time series regress...Read more...

Hidehiko Ichimura and Oliver Linton

We investigate the performance of a class of semiparametric estimators of the treatment effect via asymptotic expansions. We derive approximations to the first two moments of the estimator that are valid to 'second order...Read more...

Xiaohong Chen, Oliver Linton and Ingrid Van Keilegom

We provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions ...Read more...

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is complet...Read more...

February 2003

Liudas Giraitis and Peter M Robinson

September 2002

We attempt to present Denis Sargan's work in some kind of historical perspective, in two ways. First, we discuss some previous members of the Tooke Chair of Economic Science and Statistics, which was founded in 1859 and ...Read more...

Marc Henry and Peter M Robinson

Econometric interest in the possibility of long memory has developed as a flexible alternative to, or compromise between, the usual short memory or unit root prescriptions, for example in the context of modelling cointeg...Read more...

Raymond J Carroll, Oliver Linton, Enno Mammen and Zhijie Xiao

We propose a modification of kernel time series regression estimators that improves efficiency when the innovation process is autocorrelated. The procedure is based on a pre-whitening transformation of the dependent vari...Read more...

June 2002

This paper derives the asymptotic distribution of nonparametric neural network estimator of the Lyapunov exponent in a noisy system proposed by Nychka et al (1992) and others. Positivity of the Lyapunov exponent is an op...Read more...

March 2002

We study a very general setting, and propose a procedure for estimating the critical values of the extended Kolmogorov-Smirnov tests of First and Second Order Stochastic Dominance due to McFadden (1989) in the general k-...Read more...

Order selection based on criteria by Akaike (1974), AIC, Schwarz (1978), BIC or Hannan and Quinn (1979) HIC is often applied in empirical examples. They have been used in the context of order selection of weakly dependen...Read more...

February 2002

Javier Hidalgo and Peter M Robinson

We show that it is possible to adapt to nonparametric disturbance auto-correlation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum e...Read more...

September 2001

Liudas Giraitis, Javier Hidalgo and Peter M Robinson

We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency w. The case of unknown w, especially w = 0, is standard in the long memory literature. When w is unknown...Read more...

August 2001

Peter M Robinson and Yoshihiro Yajima

This paper develops methods of investigating the existence and extent of cointegration in fractionally integrated systems. We focus on stationary series, with some discussion of extension to nonstationarity. The setting ...Read more...

July 2001

D Marinucci and Peter M Robinson

Robinson and Marinucci (1998) investigated the asymptotic behaviour of a narrow-band semiparametric procedure termed Frequency Domain Least Squares (FDLS) in the broad context of fractional cointegration analysis. Here w...Read more...

The behaviour of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically s...Read more...

Fractional cointegration is viewed from a semiparametric viewpoint as a narrow-band phenomenon at frequency zero. We study a narrow-band frequency domain least squares estimate of the cointegrating vector, and related se...Read more...

Oliver Linton and Zhijie Xiao

We propose a new estimator for nonparametric regression based on local likelihood estimation using an estimated error score function obtained from the residuals of a preliminary nonparametric regression. We show that our...Read more...

June 2001

Javier Hidalgo and Yoshihiro Yajima

We frequently observe that one of the aims of time series analysts is to predict future values of the data. For weakly dependent data, when the model is known up to a finite set of parameters, its statistical properties ...Read more...

Parametric estimation is discussed in a variety of models exhibiting long-range dependence....Read more...

May 2001

Xiaohong Chen, Oliver Linton and Peter M Robinson

We discuss a number of issues in the smoothed nonparametric estimation of kernel conditional probability density functions for stationary processes. The kernel conditional density estimate is a ratio of joint and margina...Read more...

Oliver Linton, Jens Perch Nielsen and Sara van de Geer

We propose new procedures for estimating the univariate quantities of interest in both additive and multiplicative nonparametric marker dependent hazard models. We work with a full counting process framework that allows ...Read more...

February 2001

A valid asymptotic expansion for the covariance of functions of multivariate normal vectors is applied to approximate autovariances of time series generated by nonlinear transformation of Gaussian latent variates, and no...Read more...

Averaged periodogram; nonstationary processes; fractional Brownian motion....Read more...

December 2000

For a class of parametric ARCH models, Whittle estimation based on squared observations is shown to be inconsistent and asymptotically normal. Our conditions require the squares to have short memory autocorrelation, by c...Read more...

November 2000

L A Gil-Alaña and Peter M Robinson

The seasonal structure of quarterly UK and Japanese consumption and income is examined by means of fractionally-based tests proposed by Robinson (1994). These series were analysed from an autoregressive unit root viewpoi...Read more...

Steve Berry, Oliver Linton and Ariel Pakes

We provide an asymptotic distribution theory for a class of Generalized Method of Moments estimators that arise in the study of differentiated product markets when the number of observations is associated with the number...Read more...

July 2000

We stablish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable considered in Newey (1990) as well as to the distribution of a Wald st...Read more...

Douglas J Hodgson, Oliver Linton and Keith Vorkink

Adaptive estimation; capital asset pricing model; efficiency...Read more...

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intra-family component but require that observations from di...Read more...

Ramdan Dridi

We develop in this paper a general econometric methodology referred to as the Simulated Asymptotic Least Squares (SALS). It is shown that this approach provides a unifying theory for 'approximation-based' or simulation-b...Read more...

June 2000

Ramdan Dridi and Laurent Germain

Focusing on homogeneous beliefs, we can distinguish two commonly shared ideas that, i) the competition between informed traders destroys their trading profits, ii) trading with a noisy signal brings about a loss in the e...Read more...

Ramdan Dridi and Eric Renault

We develop in this paper a generalization of the Indirect Inference (II) to semi-parametric settings and termed Semi-parametric Indirect Inference (SII). We introduce a new notion of Partial Encompassing which lays the e...Read more...

May 2000

Whittle pseudo-maximum likelihood estimates of parameters for stationary time series have been found to be consistent and asumptotically normal in the presence of long-range dependence. Generalizing the definition of the...Read more...

We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the same mean, where the studentization employs such a n...Read more...

The nonparametric censored regression model, with a fixed, known censoring point (normalized to zero), is y = max[0,m(x) + e], where both the regression function m(x) and the distribution of the error e are unknown. This...Read more...

April 2000

Zongwu Cai, Jianqin Fan and Qiwei Yao

Varying-coefficient linear models arise from multivariate nonparametric regression, nonlinear time series modelling and forecasting, functional data analysis, longitudinal data analysis, and others. It has been a common ...Read more...

This paper introduces a nonparametric Granger-causality test for covariance stationary linear processes under, possibly, the presence of long-range dependence. We show that the test is consistent and has power against co...Read more...

Oliver Linton, Enno Mammen and N Nielsen

We derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function. The procedure employs a recent projection interpretation of p...Read more...

Oliver Linton, Enno Mammen, Jens Perch Nielsen and C Tanggaard

We introduce a new method for the estimation of discount functions, yield curves and forward curves from government issued coupon bonds. Our approach is nonparametric and does not assume a particular functional form for ...Read more...

Paolo Zaffaroni

Sufficient conditions for strict stationarity of ARCH(8) are established, without imposing covariance stationarity and for any specification of the conditional second moment coefficients. GARCH(p,q) as well as the case o...Read more...

March 2000

Liudas Giraitis, Peter M Robinson and Donatas Surgailis

Marcia M Schafgans

We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on 'identific...Read more...

January 2000

Liudas Giraitis, Peter M Robinson and Alexander Samarov

We study the impact of large cross-sections of contemporaneous aggregation of GARCH processes and of dynamic GARCH factor models. The results crucially depend on the shape of the cross-sectional distribution of the GARCH...Read more...

We establish valid theoretical and empirical Edgeworth expansions for density-weighted averaged derivative estimates of semiparametric index models....Read more...

October 1999

A valid Edgeworth expansion is established for the limit distribution of density-weighted semiparametric averaged derivative estimates of single index models. The leading term that corrects the normal limit varies in mag...Read more...

Fabio Busetti and Andrew C Harvey

The paper considers tests for the presence of a random walk component in a stationary or trend stationary time series and extends them to series which contain structural breaks. The locally best invariant (LBI) test is d...Read more...

December 1998

The aggregation procedure when a sample of length N is divided into blocks of length m = o(N), m ? ? and observations in each block are replaced by their sample mean, is widely used in statistical inference. Taqqu, Tever...Read more...

October 1998

Josu Artech and Peter M Robinson

There has recently been great interest in time series with long memory, namely series whose dependence decays slowly in the sense that autocovariances are not summable and the spectral density is unbounded. This concept ...Read more...

September 1998

Several semiparametric estimates of the memory parameter in standard long memory time series are now available. They consider only local behaviour of the spectrum near zero frequency, about which the spectrum is symmetri...Read more...

Semiparametric estimates of long memory seem useful in the analysis of long financial time series because they are consistent under much broader conditions than parametric estimates. However, recent large sample theory f...Read more...

August 1998

It is pointed out that two contradictory definitions of fractional Brownian motion are well established, one prevailing in the probabilistic literature, the other in the econometric literature. Each is associated with a ...Read more...

July 1998

D Marinucci

Band spectrum regression is considered for cointegrated time series with long memory innovations. The estimates we advocate are shown to be consistent when cointegrating relationships among stationary variables are inves...Read more...

Weak convergence to a form of fractional Brownian motion is established for a wide class of nonstationary fractionally integrated multivariate processes. Instrumental for the main argument is a result of some independent...Read more...

Marco Lippi and Paolo Zaffaroni

his paper deal with aggregation of AR(1) micro variables driven by a common and idiosyncratic shock with random coefficients. We provide a rigorous analysis, based on results on sums of r.v.'s with a possibly finite firs...Read more...

April 1998

The concept of cointegration has principally been developed under the assumption that the raw data vector zt is I(1) and the cointegrating residual et is I(0), but is also of interest in more general, including fractiona...Read more...

March 1998

J R McCrorie

As the exact discrete model induced by an open continuous time system depends on the continous time paths of the exogenous variables, these need to be interpolated for the purpose of estimation. We examine some recently ...Read more...

December 1997

We present a method of deriving the exact discrete model satisfied by equispaced data generated by a system of linear stochastic differential equations without implying the usual restrictions on observed discrete data th...Read more...

Ignacio Lobato and Peter M Robinson

There is frequently interest in testing that a scalar or vector time series is I(0), possibly after first- differencing or other detrending, while the I(0) assumption is also taken for granted in autocorrelation-consiste...Read more...

November 1997

In this paper, I explore ways of recapturing the efficiency property for estimators that rely on simulation. In particular, I show that this can be achieved by exploiting two-step maximum stimulated likelihood (SL) estim...Read more...

In a number of econometric models, rules of large-sample inference require a consistent estimate of f(0), where f (?) is the spectral density matrix of yt = ut?xt, for covariance stationary vectors ut, xt. Typically yt i...Read more...

October 1997

A central limit theorem is given for certain weighted sums of a covariance stationary process, assuming it is linear in martingale differences, but without any restriction on its spectrum. We apply the result to kernel n...Read more...

September 1997

C Michelacci and Paolo Zaffaroni

Unit root in output, an exceptional 2% rate of convergence, and no change in the underlying dynamics of output seems to be three stylized facts that can not go together. This paper extends the Solow-Swan growth model all...Read more...

July 1997

Asset returns have a very complicated dynamic pattern. Yet they display regularity across different assets and periods. We consider a new family of volatility models which account for such patterns, focussing in particul...Read more...

May 1997

V A Hajivassiliou and DL McFadden

The method of simulated scores (MSS) is presented for estimating limited dependent variables models (LDV) with flexible correlation structure in the unobservables. We propose simulators that are continuous in the unknown...Read more...

Andrew C Harvey, Siem Jan Koopman and J Penzer

Many series are subject to data irregularities such as missing values, outliers, structural breaks and irregular spacing. Data can also be messy, and hence difficult to handle by standard procedures, when they are intrin...Read more...

March 1997

Standard approaches to the estimation of sample selection models are known to be inconsistent under non-normality. In particular, this paper considers the two-step Heckman (1976, 1979) estimator of the interecept of the ...Read more...

This paper is an empirical study on the labor force in (Peninsular) Malaysia. It applies both parametric and semiparametric sample selection methods to the estimation of wage equations. These equations are then used to a...Read more...

This paper analyses price fixing by the Joint Executive Committee railroad cartel from 1880 to 1886 and develops tests of two game-theoretic models of tacit collusion. The first model, due to Abreu, Pearce and Stacchetti...Read more...

There exist several estimators of the memory parameter in long-memory time series models with mean µ and the spectrum specified only locally near zero frequency. In this paper we give a lower bound for the rate of conver...Read more...

February 1997

We introduce a nonlinear model of stochastic volatility within the class of ?product type? models. It allows different degrees of dependence for the ?raw? series and for the ?squared? series, for instance implying weak d...Read more...

January 1997

We discuss models that impart a form of long memory in raw time series xt or instantaneous functions thereof, in particular . on the basis of a linear or nonlinear model. The capacity of linear models for xt to imply lon...Read more...

A general limit theorem is established for time series regression estimates which include generalized least squares, in the presence of long range dependence in both errors and stochastic regressors. The setting and resu...Read more...

Recently proposed tests for unit root and other nonstationarity of Robinson (1994a) are applied to an extended version of the data set used by Nelson and Plosser (1982). Unusually, the tests are efficient (against approp...Read more...

December 1996

We consider statistical inference in the presence of serial dependence. The main focus is on use of statistics that are constructed as if no dependence were believed present, and are asymptotically normal in the presence...Read more...

Andrew C Harvey and Siem Jan Koopman

Much of economic analysis presupposes that certain economic time series can be decomposed into trends and cycles. Structural time series models are explicitly set up in terms of such unobserved components. This paper set...Read more...

March 1996

Andrew C Harvey and Mariane Streibel

A test for the presence of a stationary first-order autoregressive process embedded in white noise is constructed so as to be relatively powerful when the autoregressive parameter is close to one. This is done by setting...Read more...

Smooth nonparametric kernel density and regression estimators are studied when the data is strongly dependent. In particular, we derive Central (and Noncentral) Limit Theorems for the kernel density estimator of a multiv...Read more...

February 1996

This paper provides limit theorems for special density matrix estimators and functionals of it for a bivariate co variance stationary process whose spectral density matrix has singularities not only at the origin but pos...Read more...

Danny Quah

This paper models fluctuations in regional disaggregates as a nonstationary, dynamically evolving distribution. Doing so enables study of the dynamics of aggregate fluctuations jointly with those of the rich cross-sectio...Read more...

August 1995

Andrew C Harvey, Siem Jan Koopman and Marco Riani

A number of important economic time series are recorded on a particular day every week. Seasonal adjustment of such series is difficult because the number of weeks varies between 52 and 53 and the position of the recordi...Read more...

1995

Danny Quah and Shaun P. Vahey

In this paper, we argue that measured (RPI) inflation is conceptually mismatched with core inflation: the difference is more than just 'measurement error'. We propose a technique for measuring core inflation, based on an...Read more...

The convergence hypothesis has generated a huge empirical literature: this paper critically reviews some of the earlier key findings, clarifies their implications, and relates them to more recent results. Particular atte...Read more...

This paper reinterprets a simple model of growth and fluctuations across many economies to allow explicitly characterizing the dynamically evolving corss-economy distribution of income. Such a framework provides a more n...Read more...

1994

This paper considers unit root regressions in data having simultaneously extensive cross-section and time-series variation. The standard least-squares estimators in such data structures turn out to have an asymptotic dis...Read more...

1993

Andrew C Harvey and N.G. Shephard

A stochastic variance model may be estimated by quasi-maximum likelihood procedure by transforming to a linear state space form. The properties of observations corrected for heteroscedasticity can be derived. A model wit...Read more...

Andrew C Harvey and Andrew Scott

This paper examines the implications of treating seasonality as an unobserved component which changes slowly over time. This approach simplifies the specification of dynamic relationships by separating non-seasonal from ...Read more...

Recent tests for the convergence hypothesis derive from regressing average growth rates on initial levels: a negative initial coefficient is interpreted as convergence. These tests turn out to be plagued by Galton's clas...Read more...

James Davidson

A multivariate invariance principle is given for dependent processes exhibiting trending variances and other types of global nonstationarity. The limit processes obtained in these results are not Brownian motion, but mem...Read more...

A sufficiency condition for strong mixing in infinite order moving average processes due to Gorodetski (1977) is extended, showing how smoothness conditions on the marginal distributions can be traded off against summabi...Read more...

1992

A.C. Atkinson and N.G. Shephard

Deletion diagnostics are developed for structural time series models. These show the effect of the deletion of individual observations on residuals and on the estimates of regression parameters. The methods are extended ...Read more...

Esther Ruiz

Changes in variance or volatility over time can be modelled using stochastic volatility (SV) models. This approach is based on treating the variance as an unobservable variable, the logarithm of which is modelled as a li...Read more...

The central limit theorem in Davidson (1992a) is extended to allow cases where the variances of sequence coordinates can be tending to zero. A trade off is demonstrated between the degree of dependence (mixing size) and ...Read more...

This paper gives a generalization of an L1-convergence theorem for dependent processes due to Andrews (1988). Among the cases covered by this result are weak laws of large numbers of random sequences {X1} having moments ...Read more...

Siem Jan Koopman and N.G. Shephard

The score vector for a time series model which fits into the Gaussian state space form can be approximated by numerically differentiating the log-likelihood. If the parameter vector is of length p, this involves the runn...Read more...

Andrew C Harvey and Albert Jaeger

The stylized facts of macroeconomic time series can be presented by fitting structural time series models. Within this framework, we analyze the consequences of the widely used detrending technique popularized by Hodrick...Read more...

1991

N.G. Shephard

1990

James Davidson and Stephen Hall

1989

Jan R. Magnus and Thomas J. Rothenberg

1988

Jan R. Magnus and Bahram Pesaran

1987

1986

Asraul Hoque, Jan R. Magnus and Bahram Pesaran

Jan R. Magnus

Alberto Holly and Jan R. Magnus

1985

Jan R. Magnus and H. Neudecker

Jan R. Magnus and Alan D. Woodland

1984

Takamitsu Sawa

Risto D.H. Heijmans and Jan R. Magnus

1983

Manfred Keil

Anthony Horsley and G.M.P. Swann

1982

1981

James Davidson and Manfred Keil

Robert F. Engle

1979