Title: A regression modeling perspective on compound decision problems
Authors: Sihai Zhao - University of Illinois at Urbana-Champaign (United States) [presenting]
William Biscarri - University of Illinois at Urbana-Champaign (United States)
Abstract: Compound decision theory is a classical area of statistics that is now experiencing a resurgence of interest. Current work is dominated by empirical Bayes approaches with desirable theoretical and empirical properties. However, empirical Bayes methods are at odds with both frequentist and Bayesian philosophies, and furthermore are not flexible enough to accommodate more complicated problems. We will present a new regression modeling perspective on compound decision problems, expanding upon previous work, that interprets the James-Stein estimator as a linear regression estimator. This new perspective will motivate new flexible estimation methods that can easily incorporate auxiliary information and new inferential procedures for the resulting estimators. These new tools will be illustrated in the analysis of genomic data.