Berry--Esseen Inequalities for U -Statistics
Lyudmila V. Gadasina · Theory of Probability and Its Applications · 2004
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 $\frac{5}{3}$ for the second family of the canonical functions in the Hoeffding expansion.