Deficiencies of u-statistics of degree 2 under symmetric distributions

Hajime Yamato, Yoshihiko Maesono

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1 Citation (Scopus)


For a continuous distribution with a certain symmetry, several U-statistics of degree 2 are asymptotically as efficient as the invariant U-statistics which are UMVU estimators of estimable parameters. To see the difference between two the statistics, we evaluate the limiting risk deficiency of the U-statistic with respect to the invariant U-statistic, which is also equal to the coefficient of the reciprocal of the sample size in the ratio of their variances. For example, Gini's mean difference is asymptotically efficient for a continuous distribution which is symmetric with respect to a point on R Its limiting risk deficiency is about 1.12 for a normal distribution.

Original languageEnglish
Pages (from-to)53-66
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Issue number1
Publication statusPublished - Jan 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability


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