The variance function of the optimal estimator of the overall mean in a heteroscedastic one-way ANOVA model is dominated by positive semi-definite quadratic functions. This makes it possible to develop closely related tests on the nullity of the overall mean parameter in one-way fixed and random...

A class of self-designing clinical trials is considered which according to an effective but simple, finite learning algorithm consists of automatically adaptively planned weighted group sequential trials with a decision about rejection of the null-hypothesis at each step, but the full...