English

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

Probability 2009-12-18 v1

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.

Keywords

Cite

@article{arxiv.0912.3425,
  title  = {U-statistics and random subgraph counts: Multivariate normal approximation via exchangeable pairs and embedding},
  author = {Gesine Reinert and Adrian Röllin},
  journal= {arXiv preprint arXiv:0912.3425},
  year   = {2009}
}
R2 v1 2026-06-21T14:25:11.080Z