Title: Optimal shrinkage estimation of predictive densities under alpha--divergences
Authors: Gourab Mukherjee - University of Southern California (United States) [presenting]
Abstract: The problem of estimating the predictive density in a heteroskedastic Gaussian model under general divergence loss is considered. Based on a conjugate hierarchical set-up, we consider generic classes of shrinkage predictive densities that are governed by location and scale hyper-parameters. For any alpha-divergence loss, we propose a risk-estimation based methodology for tuning these shrinkage hyper-parameters. The proposed predictive density estimators enjoy optimal asymptotic risk properties that are in concordance with the optimal shrinkage calibration point estimation results. These alpha-divergence risk optimality properties of the proposed predictors are not shared by empirical Bayes predictive density estimators that are calibrated by traditional methods such as maximum likelihood and method of moments. We conduct several numerical studies to compare the non-asymptotic performance of our proposed predictive density estimators with other competing methods and obtain encouraging results. We demonstrate the applicability of these shrunken predictive densities for analyzing protein expression data from virus-infected cell samples.