Minimax nonparametric goodness-of-fit testing

We discuss and study minimax nonparametric goodness-of-fit testing problems under Gaussian models in the sequence space and in the functional space. The unknown signal is assumed to vanish under the null-hypothesis. We consider alternatives under two-side constraints determined by Besov norms. We present the description of the types of sharp asymptotics under the sequence space model and of the rate asymptotics under the functional model. The structures of asymptotically minimax and minimax consistent test procedures are given. These results extend recent results of the paper [12]. The results for an adaptive setting axe presented as well.