ABSTRACT
Here we develop the theme of Section 1.3, which is how to appraise and select among decision procedures. In Sections 3.2 and 3.3 we show how the important Bayes and minimax criteria can in principle be implemented. However, actual implementation is limited. Our
examples are primarily estimation of a real parameter. In Section 3.4, we study, in the context of estimation, the relation of the two major decision theoretic principles to the non-
decision theoretic principle of maximum likelihood and the somewhat out of favor principle
of unbiasedness. We also discuss other desiderata that strongly compete with decision the-
oretic optimality, in particular computational simplicity and robustness. We return to these
themes in Chapter 6, after similarly discussing testing and confidence bounds, in Chapter 4
and developing in Chapters 5 and 6 the asymptotic tools needed to say something about the
multiparameter case.
