Abstract
The asymptotic expansions of the distributions of three statistics, namely, the likelihood ratio, Wald and Rao's score statistics, are obtained for testing a subset of parameters in the generalized linear models. The asymptotic expansions are given in closed forms up to n −1 in the null case and up to n −1/2 in the nonnull case under a sequence of Pitman alternatives. It is found that the power of Wald and Rao's score tests are same up to n −1/2. Numerical examples are presented to illustrate the performance of the asymptotic null distributions.
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