Online Program

A General Framework for Empirical Bayes Estimation in Discrete Linear Exponential Family (308218)

*Trambak Banerjee, University of Southern California 
Qiang Liu, University of Texas at Austin 
Gourab Mukherjee, University of Southern California 
Wenguang Sun, University of Southern California 

Keywords: Asymptotic Optimality, Empirical Bayes, Power Series Distributions, Shrinkage estimation, Stein's discrepancy

We develop a Nonparametric Empirical Bayes (NEB) framework 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 scalable convex program, which is carefully developed based on a 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.