Geodesic
Berry--Esseen inequalities for $U$-statistics
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 151-155

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We obtain a Berry–Esseen boundary for nondegenerate $U$-statistics of power 2 constructed by independent and not necessarily identically distributed random variables assuming finiteness of the absolute third moments for the first family of the canonical functions and the absolute moments of order $\frac 53$ for the second family of the canonical functions in the Höeffding expansion.
Keywords: $U$-statistic, Berry–Esseen inequality, rate of convergence. 
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     author = {L. V. Gadasina},
     title = {Berry--Esseen inequalities for $U$-statistics},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {151--155},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a7/}
}
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L. V. Gadasina. Berry--Esseen inequalities for $U$-statistics. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 151-155. http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a7/