Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea

ESAIM: Probability and Statistics (2001)

  • Volume: 5, page 1-31
  • ISSN: 1292-8100

Abstract

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The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point x 0 ∈ ℝ , over the density functions that belong to the Sobolev class W n ( β , L ) . We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set B n . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.

How to cite

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Butucea, Cristina. "Exact adaptive pointwise estimation on Sobolev classes of densities." ESAIM: Probability and Statistics 5 (2001): 1-31. <http://eudml.org/doc/104273>.

@article{Butucea2001,
abstract = {The subject of this paper is to estimate adaptively the common probability density of $n$ independent, identically distributed random variables. The estimation is done at a fixed point $x_\{0\}\in \mathbb \{R\}$, over the density functions that belong to the Sobolev class $W_n(\beta ,L)$. We consider the adaptive problem setup, where the regularity parameter $\beta $ is unknown and varies in a given set $B_\{n\}$. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.},
author = {Butucea, Cristina},
journal = {ESAIM: Probability and Statistics},
keywords = {density estimation; exact asymptotics; pointwise risk; sharp adaptive estimator; sharp adaptive estimators},
language = {eng},
pages = {1-31},
publisher = {EDP-Sciences},
title = {Exact adaptive pointwise estimation on Sobolev classes of densities},
url = {http://eudml.org/doc/104273},
volume = {5},
year = {2001},
}

TY - JOUR
AU - Butucea, Cristina
TI - Exact adaptive pointwise estimation on Sobolev classes of densities
JO - ESAIM: Probability and Statistics
PY - 2001
PB - EDP-Sciences
VL - 5
SP - 1
EP - 31
AB - The subject of this paper is to estimate adaptively the common probability density of $n$ independent, identically distributed random variables. The estimation is done at a fixed point $x_{0}\in \mathbb {R}$, over the density functions that belong to the Sobolev class $W_n(\beta ,L)$. We consider the adaptive problem setup, where the regularity parameter $\beta $ is unknown and varies in a given set $B_{n}$. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.
LA - eng
KW - density estimation; exact asymptotics; pointwise risk; sharp adaptive estimator; sharp adaptive estimators
UR - http://eudml.org/doc/104273
ER -

References

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