Accuracy Representations and Estimates


This document goes through some standard results about strictly proper measures of accuracy and representation theorems (Schervish and Savage/Bregman). It also presents the slightly less well studied case of measuring the accuracy of estimates of random variables. The spirit of the document is to include proofs, but to make things simple in order to make the central ideas of the proofs across, often at the cost of generality. A number of restrictive assumptions are made throughout. Full analysis of what restrictions can be dropped in the estimates case requires further work.