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September, 1994 Monotonicity Properties of the Power Functions of Likelihood Ratio Tests for Normal Mean Hypotheses Constrained by a Linear Space and a Cone
Xiaomi Hu, F. T. Wright
Ann. Statist. 22(3): 1547-1554 (September, 1994). DOI: 10.1214/aos/1176325642

Abstract

Anderson studied the monotonicity of the integral of a symmetric, unimodal density over translates of a symmetric convex set. Restricting attention to elliptically contoured, unimodal densities, Mukerjee, Robertson and Wright weakened the assumption of symmetry on the set and obtained monotonicity properties of power functions, including unbiasedness, for some likelihood ratio tests in order restricted inference for the variance-known case. For elliptically contoured, unimodal densities, we weaken the assumption of convexity to obtain similar results in the case of unknown variances. The results apply to situations in which the null hypothesis is a linear space and the alternative is a closed, convex cone.

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Xiaomi Hu. F. T. Wright. "Monotonicity Properties of the Power Functions of Likelihood Ratio Tests for Normal Mean Hypotheses Constrained by a Linear Space and a Cone." Ann. Statist. 22 (3) 1547 - 1554, September, 1994. https://doi.org/10.1214/aos/1176325642

Information

Published: September, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0818.62056
MathSciNet: MR1311989
Digital Object Identifier: 10.1214/aos/1176325642

Subjects:
Primary: 62F03
Secondary: 62H15

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 3 • September, 1994
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