An Optimal Transportation Approach for Improved Confidence Intervals

2026-06-20

AI Summary

This work addresses the poor coverage performance of traditional confidence intervals in small-sample settings or with complex models, where reliance on asymptotic approximations often fails. The authors propose a novel confidence interval construction grounded in optimal transport theory, which minimizes coverage bias through optimal coupling and incorporates data-driven hyperparameter selection to enhance practical applicability. By moving beyond conventional quantile-based approaches, the method achieves substantially improved coverage accuracy and robustness across a range of estimation problems. The theoretical analysis rigorously establishes results concerning comparisons of probability measures, consistency, and finite-sample error bounds, providing a solid foundation for the proposed framework.

Abstract

Optimal transport methods have recently attracted a lot of attention in statistics. Their appeal lies in providing a geometric framework for comparing probability measures, leading to new perspectives on classical problems. A central problem in statistics is the construction of valid confidence sets as fundamental inferential tools in practice. A well-known problem is that for complex problems or relatively small samples, their asymptotic approximations often show poor performance. This suggests to apply optimal transport methods when constructing confidence sets for hard problems to improve their coverage properties. We introduce such a procedure, derive the theoretical framework studying consistency and error bounds for the coverage probability of the resulting intervals. To guarantee feasibility in practice, we propose data-driven choices for our hyper parameters. This approach extends classical quantile-based confidence intervals by leveraging optimal couplings to minimize coverage deviations. Simulations demonstrate striking performance in different estimation problems, outperforming standard methods in accuracy and robustness.

Problem

• confidence intervals
• optimal transport
• coverage probability
• small samples
• asymptotic approximation

Innovation

• optimal transport
• confidence intervals
• coverage probability
• optimal couplings
• data-driven hyperparameters