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Adaptive estimation of a density function using beta kernels

Published online by Cambridge University Press:  08 October 2014

Karine Bertin  and
Nicolas Klutchnikoff
Karine Bertin
Affiliation:
CIMFAV, Universidad de Valparaíso, Av. Pedro Montt, 2421 Valparaíso, Chile. [email protected]
Nicolas Klutchnikoff
Affiliation:
CREST (ENSAI) et IRMA (UMR 7501 Université de Strasbourg et CNRS), Campus de Ker-Lann, Rue Blaise Pascal, BP 37203, 35172 BRUZ cedex, France; [email protected]
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Abstract

In this paper we are interested in the estimation of a density − defined on a compact interval ofℝ− from n independent andidentically distributed observations. In order to avoid boundary effect, beta kernelestimators are used and we propose a procedure (inspired by Lepski’s method) in order toselect the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimaxframework. Our estimator is compared with both the cross-validation algorithm and theoracle estimator using simulated data.

Keywords

Beta kernelsadaptive estimationminimax ratesHölder spaces
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 400 - 417
Copyright
© EDP Sciences, SMAI 2014

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