Isotonic tests for spread and tail |
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Authors: | Takemi Yanagimoto Masaaki Sibuya |
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Institution: | (1) IMB Japan, Scientific Center, Japan |
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Abstract: | 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.
The Institute of Statistical Mathematics |
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Keywords: | |
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