TY - JOUR

T1 - Deficiencies of u-statistics of degree 2 under symmetric distributions

AU - Yamato, Hajime

AU - Maesono, Yoshihiko

PY - 1989/1

Y1 - 1989/1

N2 - 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.

AB - 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.

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U2 - 10.1080/03610928908829884

DO - 10.1080/03610928908829884

M3 - Article

AN - SCOPUS:84954667800

VL - 18

SP - 53

EP - 66

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 1

ER -