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Similar Tests and the Standardized Log Likelihood Ratio Statistic

J. L. Jensen
Biometrika
Vol. 73, No. 3 (Dec., 1986), pp. 567-572
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2336520
Stable URL: http://www.jstor.org/stable/2336520
Page Count: 6
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Similar Tests and the Standardized Log Likelihood Ratio Statistic
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Abstract

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 is 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.

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