2009 ISIT Shannon Lecture
Professor Jorma Rissanen
University of Tampere
Abstract: In this talk we give a common theory of estimation of real-valued parameters, their number, and even of their structure. The same theory includes also optimal estimation of intervals. Although no “true” data generating distribution is assumed the theory may be viewed as an extension and generalization of the customary theory of estimation of real-valued parameters due to Fisher, Cramer, Rao, and others.
The central concept is estimation capacity, analogous to but different from Shannon’s channel capacity, which defines the estimator. It also defines a criterion for computing the estimates which amounts to an application of complete minimum description length principle. Theorems for mathematically defined optimality properties are given. No comparable theory - we think - is possible without basic information and coding theory.