Adaptive estimation of a density function using beta kernels

Karine Bertin; Nicolas Klutchnikoff

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 400-417
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Bertin, Karine, and Klutchnikoff, Nicolas. "Adaptive estimation of a density function using beta kernels." ESAIM: Probability and Statistics 18 (2014): 400-417. <http://eudml.org/doc/274389>.

@article{Bertin2014,
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.},
author = {Bertin, Karine, Klutchnikoff, Nicolas},
journal = {ESAIM: Probability and Statistics},
keywords = {beta kernels; adaptive estimation; minimax rates; Hölder spaces},
language = {eng},
pages = {400-417},
publisher = {EDP-Sciences},
title = {Adaptive estimation of a density function using beta kernels},
url = {http://eudml.org/doc/274389},
volume = {18},
year = {2014},
}

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
PB - EDP-Sciences
VL - 18
SP - 400
EP - 417
AB - 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.
LA - eng
KW - beta kernels; adaptive estimation; minimax rates; Hölder spaces
UR - http://eudml.org/doc/274389
ER -

References

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