D. Rodríguez Vítores, E. del Barrio Tellado, J. Loubes
The Wasserstein distance is a fundamental tool for analyzing diverse types of data, but it poses significant computational and statistical challenges in high dimensions. The sliced Wasserstein distance, based on one-dimensional projections, provides a practical alternative. Our contribution in this work is to derive a new central limit theorem for the sliced Wasserstein distance using the Efron-Stein inequality. This technique establishes a central limit theorem centered at the expected empirical value under mild conditions. Unlike for the Wasserstein distance in general dimensions, we show that under certain assumptions, the centering constant can be replaced by the population value—an essential improvement for inference. This generalizes and refines existing results for the one-dimensional case. As a result, we present the first asymptotically valid inference framework for the sliced Wasserstein distance, with p> 1, between non-compactly supported measures.
Keywords: Optimal transport, Sliced Wasserstein distance, Efron-Stein inequality, Asymptotic theory.
Scheduled
Non Parametric Statistics II
June 12, 2025 7:00 PM
Auditorio 1. Ricard Vinyes