Geodesic
Several uniform estimates of the rate of convergence in the multidimensional central limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 757-770

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In the paper some improvements of the estimates proposed in [6]–[11] are proved. 
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     author = {V. V. Senatov},
     title = {Several uniform estimates of the rate of convergence in the multidimensional central limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {757--770},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a6/}
}
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V. V. Senatov. Several uniform estimates of the rate of convergence in the multidimensional central limit theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 757-770. http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a6/