Seminario Compound selection decisions: an almost SURE approach

Abstract

This paper proposes methods for compound selection decisions in a Gaussian sequence model. Inspired by Stein's unbiased risk estimate (SURE), we introduce ASSURE, a family of estimators for welfare, defined as the expected utility of a decision rule. ASSURE enables selection of rules from a pre-specified class by Optimizing estimated welfare, thereby borrowing strength across noisy payoff estimates. A leading variant, ASSURE*, is nearly unbiased and achieves near-parametric rates, yielding decision rules with favorable regret properties conditional on unknown parameters. When the pre-specified class is derived from random-effects models for decision payoffs, these regret guarantees provide robustness to misspecification, robustifying empirical Bayes methods. We apply ASSURE to selecting Census tracts for economic mobility, identifying discriminating firms, and evaluating p-value decision rules in A/B testing.