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Minimax q risk in p balls

Cun-Hui Zhang

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Abstract

This paper provides an extension of earlier results on minimax estimation of a high-dimensional sparse vector to even more sparse vectors. Specifically, an approximation of the minimax q risk is obtained and threshold estimators are proved to achieve the minimax risk within an infinitesimal fraction in all small p balls.

Chapter information

Source
Dominique Fourdrinier, Éric Marchand and Andrew L. Rukhin, eds., Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2012), 78-89

Dates
First available in Project Euclid: 14 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1331731613

Digital Object Identifier
doi:10.1214/11-IMSCOLL806

Subjects
Primary: 62J05: Linear regression 62J07: Ridge regression; shrinkage estimators
Secondary: 62H12: Estimation 62H25: Factor analysis and principal components; correspondence analysis

Keywords
empirical Bayes compound decision rules random effects regression nonparametric estimation semiparametric estimation

Rights
Copyright © 2012, Institute of Mathematical Statistics

Citation

Zhang, Cun-Hui. Minimax ℓ q risk in ℓ p balls. Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman, 78--89, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2012. doi:10.1214/11-IMSCOLL806. https://projecteuclid.org/euclid.imsc/1331731613


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