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 ℓq risk is obtained and threshold estimators are proved to achieve the minimax risk within an infinitesimal fraction in all small ℓp balls.
Information
Published: 1 January 2012
First available in Project Euclid: 14 March 2012
Digital Object Identifier: 10.1214/11-IMSCOLL806
Subjects:
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
