Higher-order asymptotic refinements for score tests in proper dispersion models

Abstract

This paper develops second-order asymptotic theory for score tests in proper dispersion models without imposing known dispersion. Our results can be used to provide an Edgeworth expansion for the test statistic or to obtain a Bartlett-corrected statistic. The latter is a modified version of the original statistic distributed as chi-squared with an error of order View the MathML source, n being the sample size, which is an improvement over Rao's original score statistic which has a chi-squared distribution with error of order View the MathML source. We also show that the formulae we obtain generalize a number of previously published results.