The local power of the gradient test

Details The local power of the gradient test The local power of the gradient test

2010-04-30

arxiv.org/abs/1004.5543v2

Mathematics

Statistics Theory

To appear in the Annals of the Institute of Statistical Mathematics, this http://www.ism.ac.jp/editsec/aism-e.html

Scientific paper

10.1007/s10463-010-0315-4

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.

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