Second order asymptotics for score tests in generalised linear models

This paper develops finite-sample corrections for score tests in generalised linear models when the dispersion parameter is unknown, thus generalising the results of Cordeiro, Ferrari & Paula (1993). We show that the coefficients which define the Edgeworth expansion for the null distribution of the score statistic when the dispersion parameter is unknown are the coefficients obtained by these authors plus some extra terms. We also give closed-form expressions for such coefficients. An important special case of our results is the normal linear regression model. Simulation results for this model show that the corrections can be very effective, reducing the probability of conflict with other asymptotically equivalent testing criteria.