Distance between nonidentically weakly dependent random vectors and Gaussian random vectors under the bounded Lipschitz metric

This paper provides bounds for the rate of weak convergence of a multivariate weakly dependent nonidentically distributed partial sum to the Gaussian law. Using the approach of Bentkus [2003, On normal approximations, approximations of semigroups of operators, and approximations by accompanying laws. Available at the following URL: http://www.mathematik.uni-bielefeld.de/fgweb/Preprints/fg03035.pdf], we give an equivalent bound in terms of dimension, as in the case of iid random variables. The bound is stated in terms of minimal high-level assumptions.