# 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

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topBertin, 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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