Annals of Mathematical Statistics

Distribution of Likelihood Ratio in Testing Against Trend

M. T. Boswell and H. D. Brunk

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Abstract

The phrase "testing against trend" in the title refers to a situation in which observations are made with equal sample sizes on several populations belonging to a common univariate exponential family. Order relations among the parameters associated with the various populations are assumed known, and it is desired to test the null hypothesis that the parameters are all equal. The likelihood ratio test is described in Section 3. Slight extensions, developed in Section 1, of known theorems suffice to determine, in a certain sense, the asymptotic distribution of an appropriate function of the likelihood ratio. This asymptotic distribution is that of Bartholomew's combination of Chi-squares.

Article information

Source
Ann. Math. Statist., Volume 40, Number 2 (1969), 371-380.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177697701

Digital Object Identifier
doi:10.1214/aoms/1177697701

Mathematical Reviews number (MathSciNet)
MR250399

Zentralblatt MATH identifier
0255.62022

JSTOR
links.jstor.org

Citation

Boswell, M. T.; Brunk, H. D. Distribution of Likelihood Ratio in Testing Against Trend. Ann. Math. Statist. 40 (1969), no. 2, 371--380. doi:10.1214/aoms/1177697701. https://projecteuclid.org/euclid.aoms/1177697701


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