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In the construction of statistical procedures using decision theory, one primary consideration in the search for good procedures is to limit the scope of the search as much as possible. It is the purpose of this chapter to describe sufficient statistics and sufficient partitions and to indicate why, from the point of view of decision theory, one need only use those procedures which are functions of a sufficient statistic or sufficient partition. (To do this it will sometimes be necessary to use randomized statistical procedures, defined in Section 4.3.) Since a sufficient statistic is often much simpler than X itself (often 1- rather than n-dimensional), it can be a considerable saving of effort only to look at functions of a sufficient statistic rather than at all procedures (functions of X).
KeywordsRisk Function Continuous Case Discrete Case Bernoulli Random Variable Complete Class
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