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Certified Decisions
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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 $1-\alpha$ -- 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.
Forward citations
Cited by 4 Pith papers
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Robust Procurement: Bayesian Design under Worst-Case Approval Constraints
Under worst-case approval constraints, the robustly optimal procurement mechanism is Baron-Myerson with a quantity floor, and price regulation beats quantity regulation only when demand uncertainty is small at the top.
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Dynamically Consistent Statistical Decisions
Frequentist minimax rules often lack interim credibility; two axiomatized dynamically consistent criteria restore it while nesting Manski as-if and Gamma*-minimax.
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Robust Inference for Weighted Estimands
The paper constructs minimax-bias estimators and uniformly valid confidence intervals for weighted estimands by bounding differences via parameter heterogeneity and weight distance.
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When and How to Pilot: Design Rules for Two-Wave Experiments
A finite-sample decision rule that lets a pilot's variance estimates move the main-wave treatment allocation toward the Neyman allocation only as far as a confidence set allows, with a worst-case regret certificate.
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