J. Japan Statist. Soc., Vol. 31 (No. 2), pp. 225-237, 2001

Berry-Esseen Bounds for Some Statistics Including LB-Statistic and V-Statistic

Koichiro Toda and Hajime Yamato

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 of U-statistics with exact expressions.

Key words and phrases: Estimable parameter, degree, kernel, linear combination of U-statistics.

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