Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator

Yingcun Xia (), Wolfgang Karl Härdle () and Oliver Linton ()
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Yingcun Xia: National University of Singapore, Department of Statistics and Applied Probability and Risk Management Institute
Wolfgang Karl Härdle: Humboldt-Universität zu Berlin, C.A.S.E. Centre for Applied Statistics and Economics, School of Business and Economics

Chapter Chapter 11 in Exploring Research Frontiers in Contemporary Statistics and Econometrics, 2011, pp 229-261 from Springer

Abstract: 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. Xia et al. (J. Roy. Statist. Soc. B. 64:363–410, 2002) proposed an adaptive method for the multiple-index model, called MAVE. In this chapter we further refine the estimation method. Under some conditions, our estimator of the single-index is asymptotically normal and most efficient in the semi-parametric sense. Moreover, we derive higher-order 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: Link Function; Optimal Bandwidth; High Order Property; Slice Inverse Regression; Good Bandwidth (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2349-3_11

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DOI: 10.1007/978-3-7908-2349-3_11

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