The Annals of Mathematical Statistics

On the Distribution of the Likelihood Ratio

Robert V. Hogg

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Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 27, Number 2 (1956), 529-532.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177728276

Digital Object Identifier
doi:10.1214/aoms/1177728276

Mathematical Reviews number (MathSciNet)
MR79382

Zentralblatt MATH identifier
0071.13303

JSTOR
links.jstor.org

Citation

Hogg, Robert V. On the Distribution of the Likelihood Ratio. Ann. Math. Statist. 27 (1956), no. 2, 529--532. doi:10.1214/aoms/1177728276. https://projecteuclid.org/euclid.aoms/1177728276


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