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In a recent paper by the authors, a new approach--called the "embeddingmethod"--was introduced, which allows to make use of exchangeable pairs fornormal and multivariate normal approximation with Stein's method in cases wherethe corresponding couplings do not satisfy a certain linearity condition. Thekey idea is to embed the problem into a higher dimensional space in such a waythat the linearity condition is then satisfied. Here we apply the embedding toU-statistics as well as to subgraph counts in random graphs.

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