Structural adaptation via double-struck Lp-norm oracle inequalities

Alexander Goldenshluger; Oleg Lepski

doi:10.1007/s00440-007-0119-5

Structural adaptation via double-struck L_p-norm oracle inequalities

Alexander Goldenshluger
, Oleg Lepski

Department of Statistics

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

Abstract

In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary double-struck L_p-losses. These results are applied for adaptive estimation in the additive multi-index model.

Original language	English
Pages (from-to)	41-71
Number of pages	31
Journal	Probability Theory and Related Fields
Volume	143
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-007-0119-5
State	Published - Jan 2009

Bibliographical note

Funding Information:
Supported by the ISF grant No. 389/07.

Keywords

Adaptive estimation
Minimax risk
Optimal rates of convergence
Oracle inequalities
Structural adaptation

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1007/s00440-007-0119-5

Cite this

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keywords = "Adaptive estimation, Minimax risk, Optimal rates of convergence, Oracle inequalities, Structural adaptation",

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KW - Adaptive estimation

KW - Minimax risk

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KW - Oracle inequalities

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