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1971•BiometrikaRequires access

Likelihood ratio and associated test criteria

H. W. Peers

Open publisher page 111 citations

Abstract

A more accurate approximation is derived for the power function of the likelihood ratio criterion for testing a simple null hypothesis against a class of composite alternative hypotheses. Two rival test statistics suggested by Rao (1965) and asymptotically equivalent to the likelihood ratio procedure are examined and approximations are obtained to their distributions under the null and alternative hypotheses. Comparisons between the power functions of all three statistics are made.

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What this paper is about

A more accurate approximation is derived for the power function of the likelihood ratio criterion for testing a simple null hypothesis against a class of composite alternative hypotheses. Two rival test statistics suggested by Rao (1965) and asymptotically equivalent to the likelihood ratio procedure are examined and approximations are obtained to their distributions under the null and alternative hypotheses. Comparisons between the power functions of all three statistics are made.

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OpenAlex reports 111 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A more accurate approximation is derived for the power function of the likelihood ratio criterion for testing a simple null hypothesis against a class of composite alternative hypotheses. Two rival test statistics suggested by Rao (1965) and asymptotically equivalent to the likelihood ratio procedure are examined and approximations are obtained to their distributions under the null and alternative hypotheses. Comparisons between the power functions of all three statistics are made.

Key concepts: Mathematics, Likelihood-ratio test, Statistics, Score test, Ratio test, Null hypothesis, Null (SQL), Likelihood principle

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