B0823
Title: Minimax optimality of sparse Bayes predictive density estimates
Authors: Gourab Mukherjee - University of Southern California (United States) [presenting]
Abstract: The problem of predictive density estimation is studied under Kullback-Leibler loss in $\ell_0$ sparse Gaussian sequence models. We propose a proper Bayes predictive density estimate and establish its asymptotic minimaxity in sparse models. The minimax risks of predictive density estimates based on popular spike and slab approaches are also studied. Comparing our proposed Bayes predictive density estimate with thresholding based minimax optimal rules, we explain new similarities and contrasts with the parallel theory of point estimation of a multivariate normal mean under quadratic loss.
Journal