Normal approximation for generalized U-statistics and weighted random graphs

Nicolas Privault; Grzegorz Serafin

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arXiv · 2007.12811

Normal approximation for generalized U-statistics and weighted random graphs

Nicolas Privault·Grzegorz Serafin

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Abstract

We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to normal approximation for the combined weights of subgraphs in the Erd\H{o}s-R\'enyi random graph, extending the graph counting results of [1] to the setting of graph weighting. Our approach relies on a general stochastic analytic framework for functionals of independent random sequences.

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Nicolas Privault, Grzegorz Serafin. 2020-07-25. Normal approximation for generalized U-statistics and weighted random graphs. https://arxiv.org/abs/2007.12811

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