Open Access
2014 Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector
Ryan Martin, Stephen G. Walker
Electron. J. Statist. 8(2): 2188-2206 (2014). DOI: 10.1214/14-EJS949


For the important classical problem of inference on a sparse high-dimensional normal mean vector, we propose a novel empirical Bayes model that admits a posterior distribution with desirable properties under mild conditions. In particular, our empirical Bayes posterior distribution concentrates on balls, centered at the true mean vector, with squared radius proportional to the minimax rate, and its posterior mean is an asymptotically minimax estimator. We also show that, asymptotically, the support of our empirical Bayes posterior has roughly the same effective dimension as the true sparse mean vector. Simulation from our empirical Bayes posterior is straightforward, and our numerical results demonstrate the quality of our method compared to others having similar large-sample properties.


Download Citation

Ryan Martin. Stephen G. Walker. "Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector." Electron. J. Statist. 8 (2) 2188 - 2206, 2014.


Published: 2014
First available in Project Euclid: 29 October 2014

zbMATH: 1302.62015
MathSciNet: MR3273623
Digital Object Identifier: 10.1214/14-EJS949

Primary: 62C12 , 62C20 , 62F12

Keywords: data-dependent prior , fractional likelihood , high-dimensional , posterior concentration , shrinkage , two-groups model

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 2 • 2014
Back to Top