Asymptotic Normality of U-Statistics is Equivalent to Convergence in the Wasserstein Distance

2024/05/10 by M. Kroll, Kroll, Marius
Mathematics · Physics and Astronomy · #60F25. Secondary: 60G50 #Benford’s Law and Fraud Detection #FOS: Mathematics #Primary: 60F05 #Random Matrices and Applications #Statistical Mechanics and Entropy #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2405.06477

openalex publication_date 2024/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the claim in the title under mild conditions which are usually satisfied when trying to establish asymptotic normality. We assume strictly stationary and absolutely regular data.

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