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.

翻译：假设检验与置信区间在实证研究中无处不在，但它们与后续决策之间的联系往往不够清晰。我们发展了一套认证决策理论，将推荐决策与推断保证相结合。具体而言，我们为推荐行动附加P认证——即以至少$1-\alpha$概率成立的风险上界。我们证明此类认证允许下游风险规避决策者做出"安全"的风险可控采纳决策。我们进一步证明，将注意力限制于由置信集上的极小极大决策产生的P认证（即Manski（2021）所称的"基于集合估计的拟决策"）不会造成信息损失。对于从e值获得且具有无界风险的E认证决策，类似的论证同样适用。