Extremal families and systems of sufficient statistics (Q1188539)

This book is a revised and updated version of the author's thesis, Statistical models as extremal families. Aalborg Univ. (1982; Zbl 0499.62008). The main idea of the work is as follows: Given a family of statistics, how can one construct a statistical model such that those statistics are minimal sufficient? This idea leads to statistical models which are extremal in a sense of convex geometry. It turns out that typically exponential models have this property. The main difference between the new version and the previous one is that errors have been corrected, more examples have been added and the bibliography has been extended and updated.