Local power of the LR, Wald, score and gradient tests in dispersion models

Details Local power of the LR, Wald, score and gradient tests in dispersion models Local power of the LR, Wald, score and gradient tests in dispersion models

2011-02-21

arxiv.org/abs/1102.4371v1

Mathematics

Statistics Theory

Submitted for publication

Scientific paper

We derive asymptotic expansions up to order $n^{-1/2}$ for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions it is shown that there is no uniform superiority of one test with respect to the others for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes.

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