Compound Selection Decisions: An Almost SURE Approach

TL;DR

This paper introduces ASSURE, a nearly unbiased estimator inspired by SURE, for making optimal compound selection decisions in Gaussian models, with applications in economics, discrimination detection, and A/B testing.

Contribution

It develops ASSURE, a novel estimator for expected utility, enabling data-driven selection rules that outperform traditional methods in Gaussian sequence models.

Findings

ASSURE provides asymptotically optimal decision rules.

Application to Census tract selection improves economic opportunity analysis.

Method outperforms existing approaches in A/B testing scenarios.

Abstract

This paper proposes methods for producing compound selection decisions in a Gaussian sequence model. Given unknown, fixed parameters $\mu_ {1:n}$ and known $\sigma_{1:n}$ with observations $Y_i \sim \textsf{N}(\mu_i, \sigma_i^2)$, the decision maker would like to select a subset of indices $S$ so as to maximize utility $\frac{1}{n}\sum_{i\in S} (\mu_i - K_i)$, for known costs $K_i$. Inspired by Stein's unbiased risk estimate (SURE), we introduce an almost unbiased estimator, called ASSURE, for the expected utility of a proposed decision rule. ASSURE allows a user to choose a welfare-maximizing rule from a pre-specified class by optimizing the estimated welfare, thereby producing selection decisions that borrow strength across noisy estimates. We show that ASSURE produces decision rules that are asymptotically no worse than the optimal but infeasible decision rule in the pre-specified class. We apply ASSURE to the selection of Census tracts for economic opportunity, the identification of discriminating firms, and the analysis of $p$-value decision procedures in A/B testing.