Adaptive estimation of a density function using beta kernels
ESAIM: Probability and Statistics, Tome 18 (2014), pp. 400-417.

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.

DOI : 10.1051/ps/2014010
Classification : 62G05, 62G07, 62G20
Mots-clés : beta kernels, adaptive estimation, minimax rates, Hölder spaces 
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     title = {Adaptive estimation of a density function using beta kernels},
     journal = {ESAIM: Probability and Statistics},
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     year = {2014},
     doi = {10.1051/ps/2014010},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ps/2014010/}
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Bertin, Karine; Klutchnikoff, Nicolas. Adaptive estimation of a density function using beta kernels. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 400-417. doi : 10.1051/ps/2014010. http://archive.numdam.org/articles/10.1051/ps/2014010/

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