This article is cited in 2 papers

Short Communications

On the speed of convergence in the multi-dimensional central limit theorem

V. V. Sazonov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: Estimates, which are uniform with respect to the class of convex sets, of the rate of convergence in the multi-dimensional central limit theorem for a sequence of identically distributed independent random variables with finite third moments are obtained. In the particular case corresponding to distribution functions a better estimate than that given by the general theorem is obtained. An example is constructed to show that the estimate obtained in this case, in some sence, cannot be improved

Received: 09.10.1967

 English version: Theory of Probability and its Applications, 1968, 13, 188–191

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