U-statistics and random subgraph counts: Multivariate normal approximation via exchangeable pairs and embedding

2009/12/17 by Gesine Reinert, Reinert, Gesine, Adrian Röllin +1
Computer Science · Mathematics · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0912.3425

openalex publication_date 2009/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent paper by the authors, a new approach--called the "embedding method"--was introduced, which allows to make use of exchangeable pairs for normal and multivariate normal approximation with Stein's method in cases where the corresponding couplings do not satisfy a certain linearity condition. The key idea is to embed the problem into a higher dimensional space in such a way that the linearity condition is then satisfied. Here we apply the embedding to U-statistics as well as to subgraph counts in random graphs.

Citations

• A Multivariate CLT for Decomposable Random Vectors with Finite Second Moments

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