Regions of alternatives with high and low power for goodness-of-fit tests

The calculations are done within different asymptotic models specified by signal detection tests. Specific tests are Kolmogorov-Smirnov type tests, integral tests (like the Anderson and Darling test) and Rényi tests for hazard based models. The statistical meaning and interpretation of the spaces of alternatives with high power is discussed. These alternatives belong to least favorable directions of a class of statistical functionals which are linear combinations of quantile functions. For various cases their meaning is explained for parametric submodels, in particular for location alternatives.