Random Subgraph Countsand U -statistics: Multivariate Normal Approximation via Exchangeable Pairs and Embedding
نویسندگان
چکیده
In Reinert and Röllin (2009) a new approach—called the ‘embedding method’—was introduced, which allows us tomake use of exchangeable pairs for normal andmultivariate normal approximations 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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