Title: A general framework for empirical Bayes estimation in the discrete linear exponential family
Authors: Trambak Banerjee - University of Kansas (United States) [presenting]
Gourab Mukherjee - University of Southern California (United States)
Wenguang Sun - University of Southern California (United States)
Abstract: A Nonparametric Empirical Bayes (NEB) framework is developed for compound estimation in the discrete linear exponential family, which includes a wide class of discrete distributions frequently arising from modern big data applications. We propose to directly estimate the Bayes shrinkage factor in the generalized Robbins' formula via solving a convex program, which is carefully developed based on an RKHS representation of the Stein's discrepancy measure. The new NEB estimation framework is flexible for incorporating various structural constraints into the data-driven rule, and provides a unified approach to compound estimation with both regular and scaled squared error losses. We develop theory to show that the class of NEB estimators enjoys strong asymptotic properties. Comprehensive simulation studies, as well as analyses of real data examples, are carried out to demonstrate the superiority of the NEB estimator over competing methods.