Distance between nonidentically weakly dependent random vectors and Gaussian random vectors under the bounded Lipschitz metric (Q2489842)

This paper presents an estimate of the distance, under the bounded Lipschitz metric, between the partial sum of dependent nonidentically distributed \(k\)-dimensional random vectors and a Gaussian random vector. It is well known that the bounded Lipschitz metric metrizes weak convergence and is directly related to the Prokhorov distance. The presented bound is in terms of the third absolute moment of a partial sum of the original random vectors and an error related to the dependence among the random vectors. The error related to the dependence among the random vectors is expressed in terms of minimal conditions that are easy to check if we assume any of the existing and well known weak dependence conditions in the literature.