  Along the lines of Janssen's and Pfanzagl's work the testing theory for
statistical functionals is further developed for non-parametric one-sample
problems. Efficient tests for the one-sided and two-sided problems are derived
for nonparametric statistical functionals. The asymptotic power function is
calculated under implicit alternatives and hypotheses, which are given by the
functional itself, for the one- sided and two-sided cases. Under mild
regularity assumptions it is shown that these tests are asymptotic most
powerful. The combination of the modern theory of Le Cam and approximation in
limit experiments provide a deep insight into the upper bounds for asymptotic
power functions of tests for the one-sided and two-sided problems. As example
tests based on the von Mises functional are treated in nonparametric context.
