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An Extension of a Convolution Inequality forG-Monotone Functions and an Approach to Bartholomew's Conjectures

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  • Iwasa, Manabu
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    Abstract

    A variety of convolution inequalities have been obtained since Anderson's theorem. ?In this paper, we extend a convolution theorem forG-monotone functions by weakening the symmetry condition ofG-monotone functions. Our inequalities are described in terms of several orderings obtained from a cone. It is noteworthy that the orderings detect differences in directions. A special case of the orderings induces a majorization-like relation on spheres. Applying our inequality, Bartholomew's conjectures, which concern directions yielding the maximum power and the minimum power of likelihood ratio tests for order-restricted alternatives, are partly settled.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 59 (1996)
    Issue (Month): 2 (November)
    Pages: 249-271

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    Handle: RePEc:eee:jmvana:v:59:y:1996:i:2:p:249-271

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    Related research

    Keywords: Bartholomew's conjecture -test cone ordering convolution inequality G -monotone function K-decreasing function majorization order restricted alternatives reflection;

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