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J. Japan Statist. Soc., Vol. 36 (No. 1), pp. 73-89, 2006

A Convex Combination of Two-Sample U-Statistics

Koichiro Toda and Hajime Yamato

Abstract. A convex combination of one-sample U-statistics was introduced by Toda and Yamato (2001) and its Edgeworth expansion was derived by Yamato et al. (2003). We introduce a convex combination of two-sample U-statistics, which includes two-sample U-statistic, V-statistic and limit of Bayes estimate. Its Edgeworth expansion is derived with remainder term o(N-1/2, under the condition that the kernel is non-degenerate. We give some examples of the expansion for three statistics, two-sample U-statistic, V-statistic and limit of Bayes estimate, based on some distributions.

Key words and phrases: Convex combination, two-sample U-statistic, two-sample V-statistic.


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