# On the Precise Asymptotics of Universal Inference

arXiv: https://arxiv.org/abs/2503.14717 · HTML: https://mlsanity.com/paper/2503.14717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 17 of 17)

- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [There are natural scores: Full comment on Shafer, "Testing by betting: A strategy for statistical and scientific communication"](https://mlsanity.com/paper/2102.05569/) (2021)
- [Universal Inference](https://mlsanity.com/paper/1912.11436/) (2019)
- [Merging uncertainty sets via majority vote](https://mlsanity.com/paper/2401.09379/) (2024)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Randomized and Exchangeable Improvements of Markov's, Chebyshev's and Chernoff's Inequalities](https://mlsanity.com/paper/2304.02611/) (2023)
- [Dimension-agnostic inference using cross U-statistics](https://mlsanity.com/paper/2011.05068/) (2020)
- [Winners with Confidence: Discrete Argmin Inference with an Application to Model Selection](https://mlsanity.com/paper/2408.02060/) (2024)
- [Universal Inference Meets Random Projections: A Scalable Test for Log-concavity](https://mlsanity.com/paper/2111.09254/) (2021)
- [Honest Inference for Stochastic Optimization](https://mlsanity.com/paper/2501.07772/) (2025)
- [Gaussian Universal Likelihood Ratio Testing](https://mlsanity.com/paper/2104.14676/) (2021)
- [Confidence in Causal Discovery with Linear Causal Models](https://mlsanity.com/paper/2106.05694/) (2021)
- [On the choice of the splitting ratio for the split likelihood ratio test](https://mlsanity.com/paper/2203.06748/) (2022)
- [Median Regularity and Honest Inference](https://mlsanity.com/paper/2206.02954/) (2022)
- [Generalized Universal Inference on Risk Minimizers](https://mlsanity.com/paper/2402.00202/) (2024)

## Abstract (arXiv)

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.