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Biometrika 1986 73(2):333-343; doi:10.1093/biomet/73.2.333
© 1986 by Biometrika Trust
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The underlying structure of nonnested hypothesis tests

JOHN T. KENT

Department of Statistics, University of Leeds Leeds LS2 9JT, U.K.

A comparison between fitted and observed log likelihoods is used to study likelihood ratio statistics for both nested and nonnested hypothesis tests. A study of the geometry involved in the nonnested case clarifies the relationship between Cox's likelihood ratio test and the complete parametric Wald encompassing test of Mizon and Richard. Further it is shown why the asymptotic distribution of these test statistics is sometimes degenerate. Also, a new test statistic is proposed which combines the Cox and Mizon-Richard tests.

Key Words: Complete parametric Wald encompassing test • Fitted log likelihood • Kuilback-Leibler information gain • Likelihood rato test • Misspecifled hypothesis • Nonnested hypotheses • Separate families of hypotheses


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