Statistical experiments and their conical measures

Summary In the theory of functional analytic comparison of statistical experiments (started by L. LeCam) one can characterize equivalence classes of experiments by conical measures (in the sense of G. Choquet). We begin with a short proof of the (known) fact that any conical measure with normed resultant belongs to an experiment class. Then we are concerned with the special case of dominated experiments which are characterized by the extendability of their conical measures to finite concrete measures. These results are in close connection with a paper of E.N. Torgersen (Mixtures and products of dominated experiments. Ann. Statist. 5, 44–64 (1977)).After this we study class properties of experiments which are expressible in terms of their conical measures. Simple examples are domination, existence of bounded densities and compactness. It follows the investigation of a more profound class property which we call extremality and which generalizes the concept of an experiment with a sufficient and boundedly complete subalgebra. Finally we prove that the extreme points of the compact convex set of conical measures with normed resultant are just the conical measures of the extremal experiments.