Adaptive estimation of a density function using beta kernels

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2014 France Publisher:EDP SciencesJournal:ESAIM: Probability and Statistics, volume 18, pages 400-417 (issn: 1292-8100, eissn: 1262-3318,

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Authors: Bertin, Karine; Klutchnikoff, Nicolas;

doi: 10.1051/ps/2014010

handle: 10533/132733

Adaptive estimation of a density function using beta kernels

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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.

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France

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Keywords

62G07, 62G05, [MATH]Mathematics [math], 62G20

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