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Econometrics Paper
Inference on distribution functions under measurement error
Karun Adusumilli, Taisuke Otsu and Yoon-Jae Whang
November 2017
Paper No' EM 594:
Full Paper (pdf)

JEL Classification: C12; C14

Tags: measurement error; confidence band; stochastic dominance

This paper is concerned with inference on the cumulative distribution function (cdf) ∗ in the classical measurement error model = ∗ + . We show validity of asymptotic and bootstrap approximations for the distribution of the deviation in the sup-norm between the deconvolution cdf estimator of Hall and Lahiri (2008) and ∗ . We allow the density of to be ordinary or super smooth, or to be estimated by repeated measurements. Our approximation results are applicable to various contexts, such as confidence bands for ∗ and its quantiles, and for performing various cdf-based tests such as goodness-of-fit tests for parametric models of densities, two sample homogeneity tests, and tests for stochastic dominance. Simulation and real data examples illustrate satisfactory performance of the proposed methods.