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Valuing Winners: When and How to Correct for Selection Bias in Randomized Experiments

Ron Berman, Walter W. Zhang, Hangcheng Zhao

arXiv 16 May 2026 · Econometrics

arXiv:2605.18887 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Decision-makers often deploy the best-performing treatment from a randomized experiment, creating a winner's curse: selection favors treatments whose observed outcomes are high partly because of statistical noise, so the naïve estimate of the winner is upward biased. We distinguish two forms of winner's curse, bias relative to the true best treatment (global) and bias relative to the selected treatment's true mean (selective), and link them to regret from deploying a suboptimal treatment. This framework defines seven decision-relevant evaluation targets: mean bias, mean squared error, and confidence interval coverage for the global and selective winner's curse, and mean regret. We then show that methods that perform well on one target can perform poorly on others, so corrections should be matched to the manager's objective. Across simulations with varying effect sizes, multiple-arm settings, and data calibrated to an online A/B testing platform, no method dominates uniformly: the plug-in estimator performs best when treatment differences are large, cross-fitting performs best when treatments are similar, and resampling methods often achieve low mean squared error for moderate differences. We also introduce an adaptive empirical likelihood procedure that delivers asymptotically valid confidence intervals across settings without the tuning sensitivity of resampling-based methods.

Citation extraction

31
references
84
in-text mentions
31
distinct cited
3
self-citations
12,569
main-text words

appendix boundary found by appendix_command · 54% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Xu, Sikun and Thomadsen, Raphael and Zhang, Dennis (2025) The Winner's Curse in Data-Driven Decision Making: Evidence and Solutions1.00054100%
2Andrews, Isaiah and Kitagawa, Toru and McCloskey, Adam (2024) Inference on winners0.96510690%
3Fang, Zhuo and Santos, Andres (2019) Inference on Directionally Differentiable Functions0.9568488%
4Efron, Bradley and Tibshirani, Robert J (1993) An Introduction to the Bootstrap0.92843100%
5Andrews, Donald W. K (2000) Inconsistency of the Bootstrap When a Parameter is on the Boundary of the Parameter Space0.90912375%
6Smith, James E. and Winkler, Robert L (2006) The Optimizer's Curse: Skepticism and Postdecision Surprise in Decision Analysis0.84333100%
7Kuchibhotla, Arun K. and Kolassa, John E. and Kuffner, Todd A (2022) Post-Selection Inference0.81142100%
8Owen, Art B (2001) Empirical Likelihood0.7946450%
9Richard Dykstra (1991) Asymptotic Normality for Chi-Bar-Square Distributions0.7373367%
10Hong, Han and Li, Jessie (2018) The Numerical Delta Method0.73732100%

Showing the top 10 of 31 scored citations.