Optimal smoothing for a computationally and statistically efficient single index estimator

Hardle, Wolfgang, Xia, Yingcun and Linton, Oliver (2009) Optimal smoothing for a computationally and statistically efficient single index estimator. Econometrics (EM/2009/537). Suntory and Toyota International Centres for Economics and Related Disciplines, London, UK.

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Abstract

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.

Item Type:	Monograph (Report)
Official URL:	http://sticerd.lse.ac.uk/
Additional Information:	© 2009 The Authors
Divisions:	STICERD
Subjects:	H Social Sciences > HB Economic Theory
Date Deposited:	23 Jul 2014 11:58
Last Modified:	13 Sep 2024 16:40
URI:	http://eprints.lse.ac.uk/id/eprint/58173

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