  In this paper we are interested in testing whether there are any signals
hidden in high dimensional noise data. Therefore we study the family of
goodness-of-fit tests based on $\Phi$-divergences including the test of Berk
and Jones as well as Tukey's higher criticism test. The optimality of this
family is already known for the heterogeneous normal mixture model. We now
present a technique to transfer this optimality to more general models. For
illustration we apply our results to dense signal and sparse signal models
including the exponential-$\chi^2$ mixture model and general exponential
families as the normal, exponential and Gumbel distribution. Beside the
optimality of the whole family we discuss the power behavior on the detection
boundary and show that the whole family has no power there, whereas the
likelihood ratio test does.
