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

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

2009-12-17

arxiv.org/abs/0912.3425v1

Mathematics

Probability

Scientific paper

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.

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