2025/03/18 by Kenta Takatsu, Takatsu, Kenta
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Probability and Statistical Research #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2503.14717
openalex publication_date 2025/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.