Probabilities of large deviations for $U$-statistics
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 215-220

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Some theorems on the probabilities of large deviations for the sums of random variables are applied to $U$-statistics.
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T. L. Malevič; В. Abdalimov. Probabilities of large deviations for $U$-statistics. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 215-220. http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a24/