Universal pointwise selection rule in multivariate function estimation

Alexander Goldenshluger; Oleg Lepski

doi:10.3150/08-BEJ144

Universal pointwise selection rule in multivariate function estimation

Alexander Goldenshluger
, Oleg Lepski

Department of Statistics

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

Abstract

In this paper, we study the problem of pointwise estimation of a multivariate function. We develop a general pointwise estimation procedure that is based on selection of estimators from a large parameterized collection. An upper bound on the pointwise risk is established and it is shown that the proposed selection procedure specialized for different collections of estimators leads to minimax and adaptive minimax estimators in various settings.

Original language	English
Pages (from-to)	1150-1190
Number of pages	41
Journal	Bernoulli
Volume	14
Issue number	4
DOIs	https://doi.org/10.3150/08-BEJ144
State	Published - Nov 2008

Keywords

Adaptive estimation
Minimax risk
Optimal rates of convergence
Pointwise estimation

ASJC Scopus subject areas

Statistics and Probability

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10.3150/08-BEJ144

Cite this

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abstract = "In this paper, we study the problem of pointwise estimation of a multivariate function. We develop a general pointwise estimation procedure that is based on selection of estimators from a large parameterized collection. An upper bound on the pointwise risk is established and it is shown that the proposed selection procedure specialized for different collections of estimators leads to minimax and adaptive minimax estimators in various settings.",

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author = "Alexander Goldenshluger and Oleg Lepski",

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AB - In this paper, we study the problem of pointwise estimation of a multivariate function. We develop a general pointwise estimation procedure that is based on selection of estimators from a large parameterized collection. An upper bound on the pointwise risk is established and it is shown that the proposed selection procedure specialized for different collections of estimators leads to minimax and adaptive minimax estimators in various settings.

KW - Adaptive estimation

KW - Minimax risk

KW - Optimal rates of convergence

KW - Pointwise estimation

UR - https://www.scopus.com/pages/publications/58149352562

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DO - 10.3150/08-BEJ144

M3 - Article

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Universal pointwise selection rule in multivariate function estimation

Abstract

Keywords

ASJC Scopus subject areas

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