Geodesic
On the speed of convergence in the multi-dimensional central limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 191-194

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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 
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     author = {V. V. Sazonov},
     title = {On the speed of convergence in the multi-dimensional central limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     volume = {13},
     number = {1},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a19/}
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V. V. Sazonov. On the speed of convergence in the multi-dimensional central limit theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 191-194. http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a19/