On Robust Sequential Analysis - Kiefer-Weiss Optimal Testing under Interval Probability

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.