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June, 1956 On the Distribution of the Likelihood Ratio
Robert V. Hogg
Ann. Math. Statist. 27(2): 529-532 (June, 1956). DOI: 10.1214/aoms/1177728276


In an investigation of the distribution of the likelihood ratio $\lambda$, Wilks [3] proved, under certain regularity conditions, that $-2 \ln \lambda$ is, except for terms of order $1/\sqrt n$, distributed like $\chi^2$ with $k - m$ degrees of freedom, where $k$ is the dimension of the parameter space $\Omega$ of admissible hypotheses and $m$ is the dimension of the parameter space $\omega$ of null hypotheses. In this paper, we consider the nonregular densities investigated by R. C. Davis [1] and show that for certain hypotheses $-2 \ln \lambda$ has an exact $\chi^2$-distribution with $2(k - m)$ degrees of freedom.


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Robert V. Hogg. "On the Distribution of the Likelihood Ratio." Ann. Math. Statist. 27 (2) 529 - 532, June, 1956.


Published: June, 1956
First available in Project Euclid: 28 April 2007

zbMATH: 0071.13303
MathSciNet: MR79382
Digital Object Identifier: 10.1214/aoms/1177728276

Rights: Copyright © 1956 Institute of Mathematical Statistics

Vol.27 • No. 2 • June, 1956
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