arXiv 23 Dec 2020 · Econometrics · publishedEconometrica (2023) · 35 citations (OpenAlex)
arXiv:2012.12550 · PDF · DOI · OpenAlex · Extracted main text
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 of merit for $n$ objects of potentially heterogeneous precision and are asked to select a group of the objects that are "most meritorious." The problem is naturally formulated in the compound decision framework of Robbins's (1956) empirical Bayes theory, but it also exhibits close connections to the recent literature on multiple testing. The nonparametric maximum likelihood estimator for mixture models (Kiefer and Wolfowitz (1956)) is employed to construct optimal ranking and selection rules. Performance of the rules is evaluated in simulations and an application to ranking U.S kidney dialysis centers.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Efron and Morris (1973) Stein's Estimation Rule and Its Competitiors - An Empirical Bayes Approach | 0.928 | 4 | 3 | 100% |
| 2 | Henderson and Newton (2016) Making the cut: improved ranking and selection for large-scale inference | 0.737 | 3 | 3 | 67% |
| 3 | Gilraine, Gu, and McMillan (2020) A New Method for Estimating Teacher Value-Added | 0.737 | 3 | 2 | 100% |
| 4 | Polyanskiy and Wu (2020) Self-regularizing Property of Nonparametric Maximum Likelihood Estimator in Mixture Models | 0.737 | 3 | 2 | 100% |
| 5 | Chetty, Friedman, and Rockoff (2014) Measuring the impacts of teachers I: Evaluating bias in teacher value-added estimates | 0.644 | 2 | 2 | 100% |
| 6 | Chetty, Friedman, and Rockoff (2014) Measuring the impacts of teachers II: Teacher value-added and student outcomes in adulthood | 0.644 | 2 | 2 | 100% |
| 7 | Jiang and Zhang (2021) Compound Empirical Bayes Interval Estimation | 0.644 | 2 | 2 | 100% |
| 8 | Kiefer and Wolfowitz (1956) Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters | 0.644 | 2 | 2 | 100% |
| 9 | Lin, Louis, Paddock, and Ridgeway (2006) Loss Function Based Ranking in Two-Stage, Hierarchical Models | 0.644 | 2 | 2 | 100% |
| 10 | Robbins (1956) An Empirical Bayes Approach to Statistics | 0.644 | 2 | 2 | 100% |
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