A new general estimate of the rate of convergence in the central limit theorem in R.
A general theorem is proved which gives an estimate of the rate of convergence on convex sets in the multidimensional central limit theorem for identically distributed summands. The estimate depends on the distance of the boundary of the convex set from the origin (the larger the distance, the better the estimate). The estimate makes sense under minimal requirements on the moments. Furthermore, the dependence on the distribution of a summand in it is in terms of pseudo-moment type quantities which may be small even if the moments are large.
Steklov Institute of Mathematics, Academy of Sciences of USSR, Moscow 117333.
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Sazonov