Neyman–Pearson testing under interval probability by globally least favorable pairs: Reviewing Huber–Strassen theory and extending it to general interval probability

Abstract

The paper studies the extension of one of the basic problems of classical statistics to a generalized concept of probability. It is concerned with the generalized Neyman–Pearson problem, i.e. hypothesis testing when both hypotheses are described by interval probability (also called interval-valued probability or lower and upper probability). First the Huber–Strassen theorem and the literature based on it are reviewed. The assumption of two-monotonicity underlying all that work, however, excludes many models of practical interest. Therefore, the second part of the paper goes beyond Huber–Strassen theory. Results not relying on this severe restriction are derived, showing that a neat theory of hypothesis testing can be achieved in the framework of general interval probability.