Geodesic
The theorem on deviation of empirical measure and its applications
Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 159-164

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In the paper we obtain the moderate deviation theorems for the empirical measures in one- and multi-dimensional cases. The results are used in the construction of the density estimates having the best rates of convergence in a uniform metric. 
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     author = {V. D. Konakov},
     title = {The theorem on deviation of empirical measure and its applications},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     volume = {29},
     number = {1},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1984_29_1_a20/}
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V. D. Konakov. The theorem on deviation of empirical measure and its applications. Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 159-164. http://geodesic.mathdoc.fr/item/TVP_1984_29_1_a20/