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We provide a new general theorem for multivariate normal approximation onconvex sets. The theorem is formulated in terms of a multivariate extension ofStein couplings. We apply the results to a homogeneity test in dense randomgraphs and to prove multivariate asymptotic normality for certain doublyindexed permutation statistics.

Rates of convergence for multivariate normal approximation with applications to dense graphs and doubly indexed permutation statistics