ESTIMATE OF VARIANCE OF WILCOXON-MANN-WHITNEY STATISTIC

概要

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The problem of estimating the variance of the Wilcoxon-Mann-Whitney statistic is considered. Minimum variance unbiased estimator which is a U-statistic bootstrap estimator, an estimator proposed by Fligner & Policello (1981) and jackknife estimator are considered. We also consider induced estimators of the standard deviation and interval estitnates of the expectation of the Wilcoxon-Mann-Whitney statistic. By computer simulations, we conclude that bootstrap estimator is efficient for both the variance and the standard deviation in the sense of mean squared error. This is the same conclusion with Sakamoto & Shirahata (1992) where the estimating problem of variance of one-sample U-statistics is considered. It is, in addition to the above, found that the mean squared error of minimum variance unbiased estimator is small and the bias of the induced estimator is also small for the standard deviation. Fligner & Policello estimator gives accurate confidence coefficients for many cases and the jackknife estimator stands between the former two estimators and Filgner & Policello estimator.
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