On the Precise Asymptotics of Universal Inference

Kenta Takatsu

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arXiv · 2503.14717

On the Precise Asymptotics of Universal Inference

Kenta Takatsu

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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 $1-α$ 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 $1-α$ 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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Kenta Takatsu. 2025-03-18. On the Precise Asymptotics of Universal Inference. https://arxiv.org/abs/2503.14717

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