Compound Selection Decisions: An Almost SURE Approach
Lihua Lei, Assistant Professor of Economics at Stanford University
This paper proposes methods for producing compound selection decisions in a Gaussian sequence model. Given unknown, fixed parameters μ1:n and known σ1:n with observations Yi ∼ N(μi, σi^2), the decision maker would like to select a subset of indices S so as to maximize utility (1/n)Σ_{i∈S} (μi − Ki), for known costs Ki. 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.
Lihua Lei is an Assistant Professor at Stanford Graduate School of Business, an Assistant Professor of Statistics (by courtesy), and a Faculty Fellow at Institute for Economic Policy Research (SIEPR). He got his PhD in statistics at UC Berkeley, advised by Peter Bickel and Michael Jordan, and spent three years at Stanford Statistics working with Emmanuel Candès as a postdoc. His research areas include causal inference, econometrics, experimental design, conformal inference, multiple testing, network clustering, and stochastic optimization.
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