RANDOM SUBGRAPH COUNTS AND U-STATISTICS: MULTIVARIATE NORMAL APPROXIMATION VIA EXCHANGEABLE PAIRS AND EMBEDDING

Journal article

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. © Applied Probability Trust 2010.

Authors: Reinert, G; Rollin, A

• Publication status: Published
• Journal: JOURNAL OF APPLIED PROBABILITY
• Volume: 47
• Issue: 2
• Pages: 378-393
• Publication date: 2010-06-01
• DOI: 10.1239/jap/1276784898
• ISSN: 0021-9002
• Language: English
• Keywords: exchangeable pair; random graph statistics; Multivariate normal distribution; U-statistics; Stein's method