Certified Decisions
Abstract
Hypothesis tests and confidence intervals are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We develop a theory of certified decisions that pairs recommended decisions with inferential guarantees. Specifically, we attach P-certificates -- upper bounds on loss that hold with probability at least -- to recommended actions. We show that such certificates allow "safe," risk-controlling adoption decisions for ambiguity-averse downstream decision-makers. We further prove that it is without loss to limit attention to P-certificates arising as minimax decisions over confidence sets, or what Manski (2021) terms "as-if decisions with a set estimate." A parallel argument applies to E-certified decisions obtained from e-values in settings with unbounded loss.
Cite
@article{arxiv.2502.17830,
title = {Certified Decisions},
author = {Isaiah Andrews and Jiafeng Chen},
journal= {arXiv preprint arXiv:2502.17830},
year = {2025}
}