The Annals of Statistics

Monotonicity Properties of the Power Functions of Likelihood Ratio Tests for Normal Mean Hypotheses Constrained by a Linear Space and a Cone

Xiaomi Hu and F. T. Wright

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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.

Article information

Source
Ann. Statist., Volume 22, Number 3 (1994), 1547-1554.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325642

Digital Object Identifier
doi:10.1214/aos/1176325642

Mathematical Reviews number (MathSciNet)
MR1311989

Zentralblatt MATH identifier
0818.62056

JSTOR
links.jstor.org

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62H15: Hypothesis testing

Keywords
Anderson's inequality elliptically contoured densities order restricted inference unbiased tests

Citation

Hu, Xiaomi; Wright, F. T. 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 (1994), no. 3, 1547--1554. doi:10.1214/aos/1176325642. https://projecteuclid.org/euclid.aos/1176325642


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