Bartlett-type corrections for some score tests in proper dispersion models

Cordeiro and Ferrari (1991) have shown, quite generally, how to correct the score statistic such that the null distribution of the corrected statistic is equal to that of the asymptotic chi-squared distribution, plus terms of order n -3/2 n being the sample size. In the present paper, based on this approach, we derive improved score tests for testing the precision parameter and the full vector of regression parameters in proper dispersion models This class of models which were introduced by Barndorff-Nielsen and Jørgensen (1991), is interesting because it includes a considerable variety of important mudels, while fitting into the general framework of the generalized linear models and analysis of deviance. We also generalize some recent results by Cordeiro. Ferrari and Paula (1993).