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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	1-31
Nombre de pages	31
journal	ESAIM - Probability and Statistics
Volume	5
Les DOIs	https://doi.org/10.1051/ps:2001100
état	Publié - 1 janv. 2001

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10.1051/ps:2001100

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title = "Exact adaptive pointwise estimation on sobolev classes of densities",

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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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.

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KW - Exact asymptotics

KW - Pointwise risk

KW - Sharp adaptive estimator

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DO - 10.1051/ps:2001100

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Exact adaptive pointwise estimation on sobolev classes of densities

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