A Central Limit Theorem for Wasserstein type distances between two different laws

2017/10/26 by Philippe Berthet, Berthet, Philippe, Jean‐Claude Fort +3
Economics, Econometrics and Finance · Mathematics · #62G30 62G20 60F05 60F17 #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Approximation and Integration #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1710.09763

openalex publication_date 2017/10/26 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions F and G on \mathbb R. The estimator is based on the order statistics of (possibly dependent) samples of F resp. G. We prove the consistency and the asymptotic normality of our estimators. \beginitKeywords:\endit Central Limit Theorems- Generelized Wasserstein distances- Empirical processes- Strong approximation- Dependent samples.

Citations

• Central Limit Theorem for empirical transportation cost in general dimension

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