Asymptotic testing theory for generalized linear models

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Abstract
Statistical inference in generalized linear models is based on the premises that the maximum likelihood estimator of unknown parameters is consistent and asymptotically normal, and that various test statistics have a limiting x2-distribution. FAHRMEIR and KAUFMANN (1985) present mild conditions which assure consistency and asymptotic normality of the maximum likelihood estimator. In this paper it is shown that under essentially tha same conditions the likelihood ration statistic, the Wald statistics and the score statistic are asymptotically equivalent, i.e. they have the same limiting x2-distributions under the general linear hypothesis as well as under suitable sequences of alternatives. Thus, statistical inference in generalized linear models is asymptotically justified under rather weak requirements.

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