Title: | On the asymptotic properties of rank statistics for the two-sample location and scale problem (English) |

Author: | Goria, Mohamed N. |

Author: | Vorlíčková, Dana |

Language: | English |

Journal: | Aplikace matematiky |

ISSN: | 0373-6725 |

Volume: | 30 |

Issue: | 6 |

Year: | 1985 |

Pages: | 425-434 |

Summary lang: | English |

Summary lang: | Czech |

Summary lang: | Russian |

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Category: | math |

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Summary: | The equivalence of the symmetry of density of the distribution of observations and the oddness and evenness of the score-generating functions for the location and the scale problem, respectively, is established at first. Then, it is shown that the linear rank statistics with scores generated by these functions are asymptotically independent under the hypothesis of randomness as well as under contiguous alternatives in the last part of the paper. The linear and quadratic forms of these statistics are considered for testing the two-sample location-scale problem simultaneously. (English) |

Keyword: | hypothesis of randomness |

Keyword: | two-sample location-scale problem |

Keyword: | quadratic forms of linear rank statistics |

Keyword: | asymptotically independent |

Keyword: | contiguous alternatives |

Keyword: | asymptotic power |

Keyword: | alternatives of difference in location and scale |

Keyword: | score generating function |

MSC: | 62E20 |

MSC: | 62G10 |

idZBL: | Zbl 0614.62052 |

idMR: | MR0813531 |

DOI: | 10.21136/AM.1985.104172 |

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Date available: | 2008-05-20T18:28:47Z |

Last updated: | 2020-07-28 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/104172 |

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Reference: | [1] R. J. Beran: Linear rank statistics under alternatives indexed by a vector parameter.Ann. Math. Statist. 41 (1970), 1896-1905. Zbl 0231.62064, MR 0275594, 10.1214/aoms/1177696691 |

Reference: | [2] D. R. Cox D. V. Hinkley: Theoretical Statistics.London, Chapman and Hall, 1974. MR 0370837 |

Reference: | [3] B. S. Duran W. W. Tsai T. S. Lewis: A class of location-scale nonparametric tests.Biometrika 63 (1976), 11З-176. MR 0408102 |

Reference: | [4] M. N. Goria: A survey of two sample location-scale problem: asymptotic relative efficiencies of some rank tests.Statistica Neerlandica 36 (1982), 3-13. Zbl 0488.62028, MR 0653305, 10.1111/j.1467-9574.1982.tb00769.x |

Reference: | [5] J. Hájek Z. Šidák: Theory of Rank Tests.New York, Academic Press, 1967. MR 0229351 |

Reference: | [6] Y. Lepage: A combination of Wilcoxon and Ansari-Bradley statistics.Biometrika 58 (1971), 213-217. MR 0408101, 10.1093/biomet/58.1.213 |

Reference: | [7] Y. Lepage: Asymptotically optimum rank tests for contiguous location-scale alternative.Commun. Statist. Theor. Meth. A 4 (7) (1975), 671-687. MR 0403060 |

Reference: | [8] Y. Lepage: Asymptotic power efficiency for a location-scale problem.Commun. Statist. Theor. Meth., A 5 (13) (1976), 1257-1274. MR 0440789, 10.1080/03610927608827440 |

Reference: | [9] Y. Lepage: A class of nonparametric tests for location-scale parameter.Commun. Statist. Theor. Meth. A 6 (7) (1977), 649-659. MR 0448696, 10.1080/03610927708827522 |

Reference: | [10] R. H. Randles R. V. Hogg: Certain uncorrelated and independent rank statistics.JASA 66 (1971), 569-574. 10.1080/01621459.1971.10482307 |

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