Robust slippage tests

Summary The robust slippage testing problems ofk+1 approximately known simple hypotheses are formulated as the slippage testing problems ofk+1 composite hypotheses. It is shown that if there is a representativek+1-tuple (called a least favorable slippage tuple) of simple hypotheses, then maximin tests are given by the slippage analogues of the Neyman-Pearson tests for this tuple. Thek-sample case is treated concerning this subject. In the general situations that there does not exist any least favorable slippage tuple, a method for constructing tests is proposed and applied to the case that composite hypotheses are described in terms of certain capacities (ε-contamination, total variation). The variants of the derived tests are also suggested.