Empirical Bayes Selection for Value Maximization
Dominic Coey and
Kenneth Hung
Papers from arXiv.org
Abstract:
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 \emph{selection} of the best units is fundamentally easier than \emph{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.
Date: 2022-10, Revised 2025-05
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://arxiv.org/pdf/2210.03905 Latest version (application/pdf)
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2210.03905
Access Statistics for this paper
More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().