arXiv 8 Oct 2022 · Statistics — Methodology · 1 citations (OpenAlex)
arXiv:2210.03905 · PDF · DOI · OpenAlex · Extracted main text
We study the problem of selecting the best $m$ units from a set of $n$ as $m / n \to \alpha \in (0, 1)$, where noisy, heteroskedastic measurements of the units' true values are available and the decision-maker wishes to maximize the aggregate true value of the units selected. Given a parametric prior distribution, the empirical Bayes decision rule incurs $O_p(n^{-1})$ regret relative to the Bayesian oracle that knows the true prior. More generally, if the error in the estimated prior is of order $O_p(r_n)$, regret is $O_p(r_n^2)$. In this sense selection of the best units is fundamentally easier than estimation of their values. We show this regret bound is sharp in the parametric case, by giving an example in which it is attained. Using priors calibrated from a dataset of over four thousand internet experiments, we confirm that empirical Bayes methods perform well in detecting the best treatments with only a modest number of experiments.
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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 | Asaf Weinstein (2021) On Permutation Invariant Problems in Large-Scale Inference | 1.000 | 8 | 3 | 100% |
| 2 | Jiafeng Chen (2022) Empirical Bayes when estimation precision predicts parameters | 0.874 | 7 | 2 | 100% |
| 3 | Jiaying Gu and Roger Koenker (2020) Invidious comparisons: Ranking and selection as compound decisions | 0.811 | 4 | 2 | 100% |
| 4 | Raymond J Carroll and Peter Hall (1988) Optimal rates of convergence for deconvolving a density | 0.737 | 3 | 2 | 100% |
| 5 | F Richard Guo, James McQueen, and Thomas S Richardson (2020) Empirical Bayes for Large-scale Randomized Experiments: a Spectral Approach | 0.737 | 3 | 2 | 100% |
| 6 | Aad W van der Vaart (2000) Asymptotic statistics. Vol. 3 | 0.737 | 3 | 2 | 100% |
| 7 | Bradley Efron (2011) Tweedie’s formula and selection bias | 0.644 | 4 | 2 | 50% |
| 8 | Jiahua Chen (1995) Optimal rate of convergence for finite mixture models | 0.644 | 2 | 2 | 100% |
| 9 | Jack Kiefer and Jacob Wolfowitz (1956) Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters | 0.644 | 2 | 2 | 100% |
| 10 | Magne Mogstad, Joseph P Romano, Azeem M Shaikh, and Daniel Wilhelm (2024) Inference for ranks with applications to mobility across neighbourhoods and academic achievement across countries | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 66 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Optimizing Returns from Experimentation Programs | 0.405 | 1 | 1 |
| 2 | Reasonable uncertainty: Confidence intervals in empirical Bayes discrimination detection | 0.405 | 1 | 1 |