Geodesic
On the central limit theorem in $R^k$
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 425-429

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An estimate of the rate of convergence in the central limit theorem in $R^k$ for i. i. d. summands in the spirit of [1] is obtained. The difference of the present estimate from that of [1] is in the dependence of the right side of it on the distribution of a summand. This dependence now ameliorates as the number of summands increases. In the one-dimensional case a similar result was obtained in [2]. 
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     author = {V. V. Sazonov and V. G. Mirancev},
     title = {On the central limit theorem in $R^k$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {425--429},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a19/}
}
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V. V. Sazonov; V. G. Mirancev. On the central limit theorem in $R^k$. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 425-429. http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a19/