On the accuracy of normal approximation

The aim of the present paper is to obtain estimates of the speed of convergence in the central limit theorem in Rk for variation distance valid when (truncated) pseudo-moments are small enough. Together with the integral type estimates of Bhattacharya and Sweeting [5,6] the results of this paper lead to the integral type estimates in terms of pseudo-moments. Similar (but somewhat less general) results were anounced in [1].