Jackknifing a Convex Combination of One-Sample U-Statistics
As an estimator of an estimable parameter, we consider a convex combination of U-statistics (Toda and Yamato, 2001) Yn which includes U-statistic, V-statistic, S-statistic, and limit of Bayes estimate. We introduce the bias-reduced jackknifed estimator based on this convex combination. This statistic is written as a linear combination of U-statistics. From this, we know that jackknifed version of the V-statistic is not equal to the U-statistic for the degree more than or equal to three. To see the effects of jackknifing the statistic Yn, we show the difference between Yn and by the second-order deficiency. By second-order deficiency, we can not see the difference between Un and and between different two 's. Therefore, we show the differences between them by the fourth-order deficiency. We also give some examples using the V-statistic, limit of Bayes estimate, and S-statistic.