IMPROVED LIKELIHOOD RATIO TESTS FOR DISPERSION MODELS

In this paper we discuss improved likelihood ratio tests for both the parameters in the systematic component and the dispersion parameter in the class of dispersion models (Jorgensen, 1987a). General formulae for the expected likelihood ratio statistic are obtained explicitly in dispersion models, which generalize previous results by Cordeiro (1983, 1985, 1987) and Cordeiro & Paula (1989a). The practical use of the formulae is that we can derive closed-form Bartlett corrections for these models when the information matrix has a closed-form. Various Bartlett corrections are given for special models. The formulae have advantages for numerical purposes because they require only simple operations on matrices. Algebraically, they may be handled within computer systems such as REDUCE. Some numerical examples involving real data clarify the use of these formulae.