Nonparametric SURE estimates for compound decision problems

Dave Zhao, University of Illinois Urbana Champagne
Monday, December 4, 2017 - 4:00pm
Middlebush Hall 212

Abstract: We present a new approach to solving compound decision problems. We first derive the oracle separable decision rule, then directly estimate the rule's unknown parameters by minimizing a SURE estimate of its risk. Unlike existing procedures, we do not assume a parametric or semiparametric prior mixing distribution to derive the form of our estimator. We also do not require nonparametric maximum likelihood estimation of a mixing distribution, which simplifies our theoretical analysis. We apply our estimator to the classical Gaussian sequence problem, show that it can asymptotically achieve the minimum risk among all separable decision rules, and demonstrate its numerical properties in simulations. We next extend our theoretical and numerical results to certain multivariate extensions of the Gaussian sequence problem and apply our method to high-dimensional classification problems in genomics.