We extend Buja's concept of ``pseudo-capacities'', which comprises the neighbourhood models for classical probabilities commonly used in robust statistics. Although systematically developing various directions for generalizing that model, we especially show that robust statistics can be freed from the severe restriction to 2-monotone capacities by employing the more natural framework of coherent or F-probabilities. Our main new tool for doing this is to use bi-elastic instead of convex functions.
Keywords. Interval probability, robust statistics, neighbourhood models, distorted probability, pseudo-capacity, convex and bi-elastic functions.
Authors addresses:
Institut fuer Statistik
Ludwig-Maximilians-Universitaet Muenchen
Ludwigstr. 33
80539 Muenchen
E-mail addresses:
| Anton Wallner | toni@stat.uni-muenchen.de |