Random subgraph counts and 𝑼-statistics: multivariate normal approximation via exchangeable pairs and embedding

Random subgraph counts and 𝑼-statistics: multivariate normal approximation via exchangeable pairs and embedding

Gesine Reinert and Adrian Röllin

Source: J. Appl. Probab. Volume 47, Number 2 (2010), 378-393.

Abstract

In Reinert and Röllin (2009) a new approach - called the `embedding method' - was introduced, which allows us to make use of exchangeable pairs for normal and multivariate normal approximations 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.

First Page: Show

Primary Subjects: 60F05

Secondary Subjects: 62E17, 05C80

Keywords: Multivariate normal distribution; U-statistics; random graph statistics; Stein's method; exchangeable pair

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Permanent link to this document: http://projecteuclid.org/euclid.jap/1276784898
Digital Object Identifier: doi:10.1239/jap/1276784898
Zentralblatt MATH identifier: 05758476
Mathematical Reviews number (MathSciNet): MR2668495

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