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.
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}
}