OBE set estimates in classification problems

This paper explores the use of alternative estimates arising from the feasibility set of an optimal bounded ellipsoid (OBE) algorithm. The central estimator is interpretable as a least squares result, but all others in the bounding set are consistent with the observations and error bounds as well. The purpose of the present paper is to focus attention on the set estimates in an effort to stimulate further research into their utility in applications. As an example, we suggest the use of set estimates in classification problems in which the classes can be represented by distinct linear-in-parameters models, or by related sets.