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

Augustin, Thomas and Pöhlmann, S. (2001): On Robust Sequential Analysis - Kiefer-Weiss Optimal Testing under Interval Probability. Collaborative Research Center 386, Discussion Paper 261

Abstract

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.

• Item Type: Paper
• Keywords: Interval probability, imprecise probabilities, sequential testing, robustness, Kiefer-Weiss optimality, total-variation neighbourhood models, least favorable pairs, composite hypotheses
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386; Special Research Fields > Special Research Field 386
• Subjects: 500 Science > 510 Mathematics
• Language: English