A1250
Title: An optimal transportation approach of confidence intervals
Authors: Christophe Valvason - University of Geneva (Switzerland) [presenting]
Stefan Sperlich - University of Geneva (Switzerland)
Eustasio del Barrio - Universidad de Valladolid (Spain)
Abstract: Reliable inferential tools for small samples and complex statistics are crucial in empirical research and official statistics. The aim is to propose a novel approach to constructing confidence intervals based on optimal transport theory. While in the univariate case, Monge's problem reduces to the composition of the CDF and quantile function, small samples yield empirical CDFs with large jumps, making the standard transport map suboptimal. To address this, the optimal transport plan is computed between a reference distribution and a nonparametric estimate of the distribution of interest. Confidence intervals are first defined in the reference space and then transported back to the original problem. Optimal transport theory provides the theoretical foundation for the validity of this method. Simulation studies demonstrate that the approach achieves coverage probabilities closer to the nominal level and often reduces variance compared to both direct and bootstrap confidence interval estimators.
