Statistics and Data Science Seminar
Ryan Martin
UIC
Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector
Abstract: Estimating a sparse high-dimensional normal mean vector is an
important classical problem. In this talk, I will introduce a new
empirical Bayes model based on a unique data-dependent prior. I will
show that, under some conditions, our empirical Bayes posterior
distribution concentrates on balls, centered at the true mean vector,
with squared radius proportional to the frequentist minimax rate for the
given sparsity class. This result provides some new insight concerning
the fully Bayes approach to this same problem. Asymptotic minimaxity of
the corresponding empirical Bayes posterior mean is shown, and a simple
Gibbs sampling algorithm for computation will be discussed. Finally,
two simulation studies will be presented, demonstrating the strong
finite-sample performance of the proposed estimator against a variety of
popular alternatives. (This is joint work with Stephen Walker at the
University of Texas at Austin.)
Wednesday October 9, 2013 at 4:00 PM in SEO 636