Optimal Smoothing for a Computationallyand StatisticallyEfficient Single Index Estimator

Wolfgang Härdle, Oliver Linton and Yingcun Xia

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: In semiparametric models it is a common approach to under-smooth thenonparametric functions in order that estimators of the finite dimensionalparameters can achieve root-n consistency. The requirement of under-smoothingmay result as we show from inefficient estimation methods or technical difficulties.Based on local linear kernel smoother, we propose an estimation method toestimate the single-index model without under-smoothing. Under some conditions,our estimator of the single-index is asymptotically normal and most efficient in thesemi-parametric sense. Moreover, we derive higher expansions for our estimatorand 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 superiorperformance in a variety of applications.

Keywords: ADE; Asymptotics; Bandwidth; MAVE method; Semiparametricefficiency. (search for similar items in EconPapers)
Date: 2009-07
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https://sticerd.lse.ac.uk/dps/em/em537.pdf (application/pdf)

Related works:
Working Paper: Optimal smoothing for a computationally and statistically efficient 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:cep:stiecm:537

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