Random assignment processes: strong law of large numbers and De Finetti theorem

Abstract

In the framework of a random assignment process—which randomly assigns an index within a finite set of labels to the points of an arbitrary set—we study sufficient conditions for a strong law of large numbers and a De Finetti theorem. In particular, this yields a family of finite-valued nonexchangeable random variables that are conditionally independent given some other random variable, that is, they verify a De Finetti theorem. We show an application of the De Finetti theorem and the law of large numbers to an estimation problem.