Partitions, sufficiency and undominated families of probability measures
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This article is concerned with a class of statistical structures which has been introduced by Basu and Ghosh and where the underlying family of probability measures is not dominated. Using the concept of partition-inducible subfields it is shown that the intersection of arbitrarily many subfields is sufficient again. This gives rise to the notion of the coarsest sufficient subfield containing a given family of sets. This generated subfield may be calculated as a function of the minimal sufficient subfield which always exists in these structures. Finally some attention is given to invariance and sufficiency.
KeywordsProbability Measure Statistical Structure Statistical Decision Underlying Structure Invariance Principle
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- Basu, D. and Ghosh, J. K. (1969). Sufficient statistics in sampling from a finite universe,Proc. 36th Session Internat. Statist. Inst., 850–859.Google Scholar