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

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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1239/jap/1276784898

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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Role:
Author
Publisher:
Applied Probability Trust
Journal:
Journal of Applied Probability More from this journal
Volume:
47
Issue:
2
Pages:
378-393
Publication date:
2010-06-01
DOI:
Keywords:
Pubs id:
pubs:499857
UUID:
uuid:21b49b37-6e31-4000-a296-5e288d145bf7
Local pid:
pubs:499857
Source identifiers:
499857
Deposit date:
2016-04-04

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