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Biometrika 1975 62(2):451-460; doi:10.1093/biomet/62.2.451
© 1975 by Biometrika Trust
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The likelihood ratio criterion for a composite hypothesis under a local alternative

TAKESI HAYAKAWA

Institute of Statistical Mathematics Tokyo

The asymptotic expansions of the distributions of the likelihood ratio criterion and Wald's statistic are derived for a composite hypothesis under a sequence of local alternative hypotheses converging to the null hypothesis when the sample size tends to infinity. Comparisons between the two statistics are made.

Key Words: Asymptotic expansion of distribution • Composite hypothesis • Likelihood ratio test • Multivariate Edgeworth expansion • Pitman's relative efficiency • Unbiasedness • Wald statistic


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