Berry-esseen bounds for multiddimensional central limit theorem via stein's method

Abstract

We give bounds in multivariate normal approximation for multidimensional Berry-Esseen theorem. With the assumption that the random vectors have an absolute third moments but they may not be identically distributed. We obtain uniform bounds on a closed sphere, a half plane and a rectangular set and non-uniform bounds on the first two sets. The Stein’s method using concentration inequality approach is applied. Moreover, we provide constants in uniform bounds on these sets.