### Abstract

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 language | English |
---|---|

Pages (from-to) | 53-66 |

Number of pages | 14 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 18 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1989 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability

## Fingerprint Dive into the research topics of 'Deficiencies of u-statistics of degree 2 under symmetric distributions'. Together they form a unique fingerprint.

## Cite this

*Communications in Statistics - Theory and Methods*,

*18*(1), 53-66. https://doi.org/10.1080/03610928908829884