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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. karine.bertin@uv.cl
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; nicolas.klutchnikoff@ensai.fr
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Abstract

In this paper we are interested in the estimation of a density − defined on a compact interval of ℝ− from n independent and identically distributed observations. In order to avoid boundary effect, beta kernel estimators are used and we propose a procedure (inspired by Lepski’s method) in order to select the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimax framework. Our estimator is compared with both the cross-validation algorithm and the oracle 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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