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Biometrika 1971 58(3):577-587; doi:10.1093/biomet/58.3.577
© 1971 by Biometrika Trust
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Likelihood ratio and associated test criteria

H. W. PEERS

University of Leeds

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 Words: Likelihood • ratio test • Asymptotio distributions of test oriteria • Multivariate Edgeworth series • Locally most powerful test • Unbiased test


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