The local power of the efficient scores test statistic

Abstract

SUMMARY The test statistic based on the efficient scores is shown to be locally biased in general. Comparisons of the local powers of this statistic, the likelihood ratio and maximum likelihood statistics reveal no uniform superiority properties. The performance of all three criteria in testing the sphericity hypothesis is examined and conditions which result in equivalence are discussed. A second example on testing for serial correlation suggests that computational simplicity may outweigh any marginal advantage in terms of local power.