Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator

Yingcun Xia, Wolfgang Karl Härdle and Oliver Bruce Linton ()

No SFB649DP2009-028, SFB 649 Discussion Papers from Humboldt University, Collaborative Research Center 649

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.

Keywords: ADE; Asymptotics; Bandwidth; MAVE method; Semi-parametric efficiency (search for similar items in EconPapers)
JEL-codes: C00 C13 C14 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2009-05
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