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Asymptotic unbiased density estimators

Published online by Cambridge University Press:  21 February 2009

Nicolas W. Hengartner  and
Éric Matzner-Løber
Nicolas W. Hengartner
Affiliation:
Stochastics Group, Los Alamos National Laboratory, NM 87545, USA.
Éric Matzner-Løber
Affiliation:
UMR 6625, IRMAR, Université Rennes 2, 35043 France; [email protected].
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Abstract

This paper introduces a computationally tractable density estimatorthat has the same asymptotic variance as the classical Nadaraya-Watsondensity estimator but whose asymptotic bias is zero. We achieve this resultusing a two stage estimator that applies a multiplicative bias correctionto an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as n = 50, where we see an improvement of as much as 20% over the traditionnal estimator.

Keywords

Nonparametric density estimationkernel smootherasymptotic normalitybias reductionconfidence intervals
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 13 , July 2009 , pp. 1 - 14
Copyright
© EDP Sciences, SMAI, 2009

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