Volume 18, 2014
|Page(s)||400 - 417|
|Published online||08 October 2014|
Adaptive estimation of a density function using beta kernels
1 CIMFAV, Universidad de Valparaíso, Av. Pedro Montt, 2421
2 CREST (ENSAI) et IRMA (UMR 7501 Université de Strasbourg et CNRS), Campus de Ker-Lann, Rue Blaise Pascal, BP 37203, 35172 BRUZ cedex, France
Revised: 15 March 2014
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.
Mathematics Subject Classification: 62G05 / 62G07 / 62G20
Key words: Beta kernels / adaptive estimation / minimax rates / Hölder spaces
© EDP Sciences, SMAI 2014
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