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Activity Number: 657 - Bayesian and Empirical Bayes
Type: Contributed
Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #305161
Title: A General Framework for Empirical Bayes Estimation in the Discrete Linear Exponential Family
Author(s): Trambak Banerjee* and Qiang Liu and Gourab Mukherjee and Wenguang Sun
Companies: University of Southern California and University of Texas at Austin and University of Southern California and University of Southern California
Keywords: Asymptotic Optimality; Empirical Bayes; Power Series Distributions; Shrinkage estimation; Stein’s discrepancy; U-Statistics

We develop a novel Non-parametric Empirical Bayes (NEB) estimation framework for simultaneous estimation of the power parameters in the Discrete Linear Exponential family. The NEB framework can handle a wide range of discrete distributions than previously proposed and relies on efficient estimation of the shrinkage magnitudes that appear in the Bayes decision rule for estimating the power parameters in the aforementioned family. The estimated shrinkage magnitudes are asymptotically unbiased and involve minimizing a kernelized representation of Stein`s discrepancy for discrete distributions through a scalable convex program that can incorporate structural constraints, like monotonicity, in the resulting decision rule. A thorough study of the Poisson and Binomial compound decision problem is presented to illustrate the estimation framework. Our theoretical results show that the proposed NEB estimator is asymptotically optimal, while a comprehensive simulation study as well as real data examples illustrate the efficacy of our method when compared to existing shrinkage estimators.

Authors who are presenting talks have a * after their name.

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