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Isotonic tests for spread and tail

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Summary

One-sample test problem for ‘stochastically more (or less) spread’ is defined and a family of tests with isotonic power is given. The problem is closely related to that for ‘longer (or shorter) tail’ in the reliability theory and the correspondence between them is shown.

To characterize the tests three spread preorders inR n and corre-sponding tail preorders inR n+ are introduced. Functions which are ‘monotone’ in these orders, and subsets which are ‘centrifugal’ or ‘centripetal’ with respect to these orders are studied. These notions generalize the Schur convexity.

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Authors and Affiliations

  1. IMB Japan, Scientific Center, Japan

    Takemi Yanagimoto & Masaaki Sibuya

Authors
  1. Takemi Yanagimoto
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  2. Masaaki Sibuya
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The Institute of Statistical Mathematics

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Yanagimoto, T., Sibuya, M. Isotonic tests for spread and tail. Ann Inst Stat Math 28, 329–342 (1976). https://doi.org/10.1007/BF02504750

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  • DOI: https://doi.org/10.1007/BF02504750

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