Exact adaptive pointwise estimation on sobolev classes of densities

Cristina Butucea

doi:10.1051/ps:2001100

Exact adaptive pointwise estimation on sobolev classes of densities

Cristina Butucea

Université Paris-Nanterre

Research output: Contribution to journal › Article › peer-review

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 x₀ ε 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.

Original language	English
Pages (from-to)	1-31
Number of pages	31
Journal	ESAIM - Probability and Statistics
Volume	5
DOIs	https://doi.org/10.1051/ps:2001100
Publication status	Published - 1 Jan 2001

Keywords

Density estimation
Exact asymptotics
Pointwise risk
Sharp adaptive estimator

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10.1051/ps:2001100

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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 x0 ε R, over the density functions that belong to the Sobolev class Wn(β, L). We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set Bn. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.",

keywords = "Density estimation, Exact asymptotics, Pointwise risk, Sharp adaptive estimator",

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N2 - 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 x0 ε R, over the density functions that belong to the Sobolev class Wn(β, L). We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set Bn. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.

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 x0 ε R, over the density functions that belong to the Sobolev class Wn(β, L). We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set Bn. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.

KW - Density estimation

KW - Exact asymptotics

KW - Pointwise risk

KW - Sharp adaptive estimator

U2 - 10.1051/ps:2001100

DO - 10.1051/ps:2001100

M3 - Article

AN - SCOPUS:84858745362

SN - 1292-8100

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SP - 1

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JO - ESAIM - Probability and Statistics

JF - ESAIM - Probability and Statistics

ER -

Exact adaptive pointwise estimation on sobolev classes of densities

Abstract

Keywords

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