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Abstract:

Econometrics Paper
Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator
Wolfgang Härdle, Oliver Linton and Yingcun Xia July 2009
Paper No' EM/2009/537:
Full Paper (pdf)

Tags: ade; asymptotics; bandwidth; mave method; semiparametric efficiency.

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-smoothing may result as we show from inefficient estimation methods or technical difficulties. Based on local linear kernel smoother, we propose an estimation method to estimate the single-index model without under-smoothing. Under some conditions, our estimator of the single-index is asymptotically normal and most efficient in the semi-parametric sense. Moreover, we derive higher expansions for our estimator and use them to define an optimal bandwidth for the purposes of index estimation. As a result we obtain a practically more relevant method and we show its superior performance in a variety of applications.