Titlebook: Statistical Decision Theory; Foundations, Concept James O. Berger Book 19801st edition Springer Science+Business Media New York 1980 Analys

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Complete and Essentially Complete Classes,and easy to use, and is only slightly inadmissible.) It is, therefore, of interest to find, for a given problem, the class of acceptable (usually admissible) decision rules. Such a class is often much easier to work with, say in finding a minimax or a Γ-minimax decision rule, than is the class of al

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Utility and Loss,s “name” product in discount stores. The immediate profit which would accrue from increased sales is relatively easy to estimate, but the longterm effect of a decrease in prestige is much harder to deal with.

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Minimax Analysis, axioms. We are left in the uncomfortable position of asking why this chapter is of any interest. (Indeed many Bayesians will deny that it is of any interest.) It thus behooves us to start with a discussion of when minimax analysis can be useful.

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Invariance,rence. Many of the key ideas in these approaches will, however, be brought out in the discussion of invariance and its relationship to the use of noninformative priors. The basic idea of invariance is best conveyed through an example.

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Complete and Essentially Complete Classes,l decision rules. In this chapter, we discuss several of the most important situations in which simple reduced classes of decision rules have been obtained. Unfortunately, the subject tends to be quite difficult mathematically, and so we will be able to give only a cursory introduction to some of the more profound results.

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