On the Precise Asymptotics of Universal Inference

• URL: http://arxiv.org/abs/2503.14717v1
• Date: Tue, 18 Mar 2025 20:41:00 GMT
• Title: On the Precise Asymptotics of Universal Inference
• Abstract summary: This manuscript studies the gap between validity and conservativeness, using universal inference (Wasserman et al., 2020)<n>We identify the source of conservativeness and propose a general remedy based on studentization and bias correction.<n>The resulting method attains exact coverage at the nominal $1-alpha$ level, even under model misspecification.
• Score: 1.0878040851638
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to elusive constants, leading to extreme conservativeness, where the empirical coverage probability of nominal $1-\alpha$ level confidence sets approaches one. This manuscript studies this gap between validity and conservativeness, using universal inference (Wasserman et al., 2020) with a regular parametric model under model misspecification as a running example. We identify the source of asymptotic conservativeness and propose a general remedy based on studentization and bias correction. The resulting method attains exact asymptotic coverage at the nominal $1-\alpha$ level, even under model misspecification, provided that the product of the estimation errors of two unknowns is negligible, exhibiting an intriguing resemblance to double robustness in semiparametric theory.

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