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Biometrika 1986 73(3):567-572; doi:10.1093/biomet/73.3.567
© 1986 by Biometrika Trust
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Similar tests and the standardized log likelihood ratio statistic

J. L. JENSEN

Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus DK-8000 Aarhus C, Denmark

When testing an affine hypothesis in an exponential family the ‘ideal’ procedure is to calculate the exact similar test, or an approximation to this, based on the conditional distribution given the minimal sufficient statistic under the null hypothesis. By contrast to this there is a ‘primitive’ approach in which the marginal distribution of a test statistic considered and any nuisance parameter appearing in the test statistic is replaced by an estimate. We show here that when using standardized likelihood ratio statistics the ‘primitive’ procedure is in fact an ‘ideal‘ procedure to order O(n–3/2). As an example we consider inference for the mean of a log normal distribution in detail.

Key Words: Asymptotic expansion • Bartlett adjustment • Conditional distribution • Log normal distribution


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[Abstract] [PDF]


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