Optimal smoothing for a computationally and statistically efficient single index estimator

Wolfgang Hardle, Yingcun Xia and Oliver Linton

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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; semiparametric efficiency (search for similar items in EconPapers)
JEL-codes: J1 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2009-07
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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http://eprints.lse.ac.uk/58173/ Open access version. (application/pdf)

Related works:
Working Paper: Optimal Smoothing for a Computationallyand StatisticallyEfficient Single Index Estimator (2009)
Working Paper: Optimal smoothing for a computationally and statistically efficient single index estimator (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:58173

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