The Annals of Statistics

A Probability Inequality for Elliptically Contoured Densities with Applications in Order Restricted Inference

Hari Mukerjee, Tim Robertson, and F. T. Wright

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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.

Article information

Source
Ann. Statist., Volume 14, Number 4 (1986), 1544-1554.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350175

Digital Object Identifier
doi:10.1214/aos/1176350175

Mathematical Reviews number (MathSciNet)
MR868317

Zentralblatt MATH identifier
0609.62086

JSTOR
links.jstor.org

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 60E15: Inequalities; stochastic orderings

Keywords
Anderson's inequality elliptically contoured densities order restricted tests monotonicity power functions

Citation

Mukerjee, Hari; Robertson, Tim; Wright, F. T. A Probability Inequality for Elliptically Contoured Densities with Applications in Order Restricted Inference. Ann. Statist. 14 (1986), no. 4, 1544--1554. doi:10.1214/aos/1176350175. https://projecteuclid.org/euclid.aos/1176350175


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