Sequential fixed size confidence regions for regression parameters in generalized linear models

Sequential procedures for constructing fixed size confidence regions for regression parameters in generalized linear models using maximum likelihood estimators are proposed in this paper. We consider the cases of natural link function (l.f.) and nonnatural l.f., separately. Stopping times are proposed when the scale parameter is known and unknown. In either case, the asymptotic consistency and efficiency of the sequential procedures are established under regularity conditions similar to those in Fahrmeir and Kaufmann (1985). Moreover, when the scale parameter is known, we establish the asymptotic normality of the appropriately standardized stopping time.