Invidious Comparisons: Ranking and Selection as Compound Decisions

There is an innate human tendency, one might call it the “league table mentality,” to construct rankings. Schools, hospitals, sports teams, movies, and myriad other objects are ranked even though their inherent multi‐dimensionality would suggest that—at best—only partial orderings were possible. We consider a large class of elementary ranking problems in which we observe noisy, scalar measurements merit for n potentially heterogeneous precision asked select group that “most meritorious.” The problem naturally formulated compound decision framework Robbins's (1956) empirical Bayes theory, but also exhibits close connections recent literature on multiple testing. nonparametric maximum likelihood estimator mixture models (Kiefer Wolfowitz (1956)) employed optimal selection rules. Performance rules evaluated simulations application U.S. kidney dialysis centers.