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As an estimator of an estimable parameter, Toda and Yamato (2001) introduced a linear combination Yn of U-statistics which includes V-statistic and LB-statistic. We give the Edgeworth expansions of the standardized Yn statistic with remainder o(n−1) in case that the kernel is not degenerate. We also give the Edgeworth expansions of the studentized Yn statistic using a jackknife variance estimator with remainder o(n−1/2).

Edgeworth Expansions of Some Statistics Including the LB-statistic and V-statistic