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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.
@article{PS_2014__18__400_0,
author = {Bertin, Karine and Klutchnikoff, Nicolas},
title = {Adaptive estimation of a density function using beta kernels},
journal = {ESAIM: Probability and Statistics},
pages = {400--417},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2014010},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2014010/}
}
TY - JOUR AU - Bertin, Karine AU - Klutchnikoff, Nicolas TI - Adaptive estimation of a density function using beta kernels JO - ESAIM: Probability and Statistics PY - 2014 SP - 400 EP - 417 VL - 18 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps/2014010/ DO - 10.1051/ps/2014010 LA - en ID - PS_2014__18__400_0 ER -
%0 Journal Article %A Bertin, Karine %A Klutchnikoff, Nicolas %T Adaptive estimation of a density function using beta kernels %J ESAIM: Probability and Statistics %D 2014 %P 400-417 %V 18 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps/2014010/ %R 10.1051/ps/2014010 %G en %F PS_2014__18__400_0
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
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