AN EDGEWORTH EXPANSION OF A LINEAR COMBINATION OF U-STATISTICS

抄録

In this paper we obtain an approximation of a jackknife estimator of the variance of a linear combination of U-statistics and obtain an approximation of a studentized linear combination statistic substituting the jackknife estimator of the variance. Additionally, an Edgeworth expansion with a remainder term of o(n^-1) is established for the studentized linear statistic. It is shown that both the studentized U-statistic and the von Mises V-statistic have same Edgeworth expansion.