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

Abstract

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.

Published at http://dx.doi.org/10.3150/14-BEJ639 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (4)

• Graph limits and exchangeable random graphs
• Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
• Multivariate normal approximation using exchangeable pairs
• Stein couplings for normal approximation

Cited by in corpus (1)

• Berry-Esseen bounds in the inhomogeneous Curie-Weiss model with external field