Rates of convergence for multivariate normal approximation with   applications to dense graphs and doubly indexed permutation statistics
  We provide a new general theorem for multivariate normal approximation on convex sets. The theorem is formulated in terms of a multivariate extension of Stein couplings. We apply the results to a homogeneity test in dense random graphs and to prove multivariate asymptotic normality for certain doubly indexed permutation statistics. 
Xiao Fang, Adrian R\"ollin
math.PR