Neyman-Pearson Testing under Interval Probability by Globally Least Favorable Pairs: A Survey of Huber-Strassen Theory and Some Results on its Extension to General Interval Probability.
Collaborative Research Center 386, Discussion Paper 172
The paper studies the extension of one of the basic issues of classical statistics to interval probability. It is concerned with the Generalized Neyman-Pearson problem, i.e. an alternative testing problem where both hypotheses are described by interval probability. First the Huber-Strassen theorem and the literature based on it is reviewed. Then some results are presented indicating that the restrictive assumption of C-probability (two-monotonicity) underlying all that work can be overcome in favor of considering general interval probability in the sense of Weichselberger (1999A). So the full expressive power, which is provided by interval probability, can also be utilized in testing hypotheses.