A1689
Title: Compound selection decisions: An almost SURE approach
Authors: Kevin Chen - ()
Lihua Lei - Stanford University (United States)
Timothy Sudijono - Stanford University (United States)
Tian Xie - University College London (United Kingdom)
Liyang Sun - UCL and CEMFI (Spain) [presenting]
Abstract: Methods are proposed for compound selection decisions in a Gaussian sequence model. Given unknown, fixed parameters $\mu_{1:n}$, known $\sigma_{1:n}$, observations $Y_i \sim \text{Norm}(\mu_i, \sigma_i^2)$, and known costs $k_i$, the decision maker chooses thresholds $\delta_i$ to maximize $\frac{1}{n} \sum_{i=1}^n \mathbb{1}(Y_i > \delta_i) (\mu_i - k_i)$. Inspired by Stein's unbiased risk estimate (SURE), a family of estimators termed ASSURE is introduced for the expected utility of a set of proposed thresholds. ASSURE enables practitioners to select thresholds within a pre-specified class by maximizing an estimated objective, borrowing strength across noisy estimates in compound settings. A leading member of this family, ASSURE*, is nearly unbiased for the true expected utility and converges at near-parametric rates. ASSURE* has favorable regret properties. Applications include 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.
