Certified Decisions

Isaiah Andrews and Jiafeng Chen

Papers from arXiv.org

Abstract: Hypothesis tests and confidence sets are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We view statistical inference as pairing recommended decisions with guarantees of their quality---or certificates---and develop a theory of certified decisions. Specifically, we attach P-certificates---upper bounds on loss that hold with probability at least $1-\alpha$---to recommended actions. We prove that it is without loss to limit attention to P-certificates generated by minimax decisions over confidence sets, or what Manski (2021) terms "as-if decisions with a set estimate." We further show that such certificates allow safe adoption decisions for ambiguity-averse downstream decision-makers. A parallel argument applies to E-certified decisions obtained from e-values in settings with unbounded loss. We illustrate this view of statistical inference through an application to economic mobility and one to AI model routing.

Date: 2025-02, Revised 2026-10
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