Augustin, Thomas; Pöhlmann, S.
On Robust Sequential Analysis - Kiefer-Weiss Optimal Testing under Interval Probability.
Sonderforschungsbereich 386, Discussion Paper 261
Usual sequential testing procedures often are very sensitive against even small deviations from the `ideal model' underlying the hypotheses. This makes robust procedures highly desirable. To rely on a clearly defined optimality criterion, we incorporate robustness aspects directly into the formulation of the hypotheses considering the problem of sequentially testing between two interval probabilities (imprecise probabilities). We derive the basic form of the Kiefer-Weiss optimal testing procedure and show how it can be calculated by an easy-to-handle optimization problem. These results are based on the reinterpretation of our testing problem as the task to test between nonparametric composite hypotheses, which allows to adopt the framework of Pavlov (1991). From this we obtain a general result applicable to any interval probability field on a finite sample space, making the approach powerful far beyond robustness considerations, for instance for applications in artificial intelligence dealing with imprecise expert knowledge.