AN EDGEWORTH EXPANSION OF A CONVEX COMBINATION OF U-STATISTICS BASED ON STUDENTIZATION

As an estimator of an estimable parameter, Toda and Yamato (2001) introduce Y-statistic which is a convex combination of U-statistics including V-statistic and LB-statistic. We give the Edgeworth expansions of studentized Y-statistic about the estimable parameter using a jackknife variance estimator, with remainder o(n−1).