Normal approximation for generalized U-statistics and weighted random\n graphs

2020/07/24 by Nicolas Privault, Privault, Nicolas, Grzegorz Serafin +1
Computer Science · Decision Sciences · Environmental Science · Mathematics · #05C80 #60F05 #60G50 #60H07 #FOS: Mathematics #Heavy Metal Exposure and Toxicity #Limits and Structures in Graph Theory #Multi-Criteria Decision Making #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2007.12811

openalex publication_date 2020/07/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We derive normal approximation bounds in the Wasserstein distance for sums of\nweighted U-statistics, based on a general distance bound for functionals of\nindependent random variables of arbitrary distributions. Those bounds are\napplied to normal approximation for the combined weights of subgraphs in the\nErd Hos-R 'enyi random graph, extending the graph counting results of [1] to\nthe setting of graph weighting. Our approach relies on a general stochastic\nanalytic framework for functionals of independent random sequences.\n

Citations

• Wasserstein-2 bounds in normal approximation under local dependence

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