BERRY-ESSEEN BOUNDS FOR SOME STATISTICS INCLUDING LB-STATISTIC AND V-STATISTIC

Abstract

Associated with an estimable parameter, we consider a linear combination of U-statistics. V-statistic and LB-statistic are its special cases. In this paper the kernel of the estimable parameter is assumed to be non-degenerate. For the difference between this linear combination and the well-known U-statistic, we derive upper bounds of its absolute moments about the origin and the mean. Using these upper bounds we show Berry-Esseen bound for the linear combination on U-statistics with exact expressions.