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Title:Optimal smoothing for a computationally and statistically efficient single index estimator PDF Logo
Authors:Xia, Yingcun
Härdle, Wolfgang Karl
Linton, Oliver
Issue Date:2009
Series/Report no.:SFB 649 discussion paper 2009,028
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.
MAVE method
Semi-parametric efficiency
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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