Open Access
VOL. 8 | 2012 Minimax q risk in p balls
Cun-Hui Zhang

Editor(s) Dominique Fourdrinier, Éric Marchand, Andrew L. Rukhin

Inst. Math. Stat. (IMS) Collect., 2012: 78-89 (2012) DOI: 10.1214/11-IMSCOLL806


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.


Published: 1 January 2012
First available in Project Euclid: 14 March 2012

Digital Object Identifier: 10.1214/11-IMSCOLL806

Primary: 62J05 , 62J07
Secondary: 62H12 , 62H25

Keywords: compound decision rules , Empirical Bayes , nonparametric estimation , random effects , regression , Semiparametric estimation

Rights: Copyright © 2012, Institute of Mathematical Statistics

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