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December, 1986 A Probability Inequality for Elliptically Contoured Densities with Applications in Order Restricted Inference
Hari Mukerjee, Tim Robertson, F. T. Wright
Ann. Statist. 14(4): 1544-1554 (December, 1986). DOI: 10.1214/aos/1176350175

Abstract

Anderson (1955) established the monotonicity of the integral of a symmetric, unimodal density over translates of a symmetric, convex set. A similar result is developed for integrals of elliptically contoured, unimodal densities over translates of an asymmetric, convex set in certain directions related to the set. This result is used to establish some monotonicity properties of the power functions of the likelihood ratio tests for determining whether or not a vector of normal means satisfies a specified ordering.

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Hari Mukerjee. Tim Robertson. F. T. Wright. "A Probability Inequality for Elliptically Contoured Densities with Applications in Order Restricted Inference." Ann. Statist. 14 (4) 1544 - 1554, December, 1986. https://doi.org/10.1214/aos/1176350175

Information

Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0609.62086
MathSciNet: MR868317
Digital Object Identifier: 10.1214/aos/1176350175

Subjects:
Primary: 62F03
Secondary: 60E15

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 4 • December, 1986
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