Erschöpftheit und Invarianz beim Vergleich von Experimenten

Summary Let E be the collection of all experiments (in the sense of LeCam) with the same index set. Using the notion of -informativity a binary relation is introduced in E, which turns out to be equivalent with various other relations of comparison studied previously. For a certain subclass of E a characterization of -informativity via randomisation kernels yields the equivalence to Blackwell's sufficiency and in the case of contraction experiments also to sufficiency in the sense of Halmos and Savage. Furthermore the concept of translation invariance is generalized to large subclasses of E. In the case of invariance the characterizing kernels can also be chosen invariant. Applications of the theory to allocation and testing problems as well as to Shannon- and Fisher-informativity illuminate the general set up. The special case of experiments with only a finite index set appears strongly related to the study of orderings in the set of all positive Radon measures on compact convex subsets of certain topological vector spaces.

---

---

Die vorliegende Arbeit wurde von der Naturwissenschaftlichen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg im SS 1968 als Habilitationsschrift angenommen.