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Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector
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.Comment: 18 pages, 3 figures, 3 table
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