Treatment Choice with Nonlinear Regret
Authors
Paper Information
-
Journal:
Biometrika -
DOI:
10.1093/biomet/asag008 -
Published:
February 04, 2026 -
Added to Tracker:
Feb 10, 2026
Abstract
Abstract Following Savage (1951) and Manski (2004), the literature of statistical treatment choice focuses on the mean of welfare regret. Ignoring other features of the regret distribution, however, can lead to a rule that is sensitive to sampling uncertainty. We propose to minimize the mean of a nonlinear transformation of regret and show that singleton rules are not essentially complete for nonlinear regret. Focusing on mean square regret, we derive closed-form fractions for finite-sample Bayes and minimax optimal rules. Our approach is grounded in decision theory and extends to limit experiments. The treatment fractions can be viewed as the strength of evidence favouring treatment. We apply our framework to a normal regression model and sample size calculations.
Author Details
Toru Kitagawa
AuthorSokbae Lee
AuthorChen Qiu
AuthorCitation Information
APA Format
Toru Kitagawa
,
Sokbae Lee
&
Chen Qiu
(2026)
.
Treatment Choice with Nonlinear Regret.
Biometrika
, 10.1093/biomet/asag008.
BibTeX Format
@article{paper862,
title = { Treatment Choice with Nonlinear Regret },
author = {
Toru Kitagawa
and Sokbae Lee
and Chen Qiu
},
journal = { Biometrika },
year = { 2026 },
doi = { 10.1093/biomet/asag008 },
url = { https://doi.org/10.1093/biomet/asag008 }
}