Annals of the Institute of Statistical Mathematics

, Volume 34, Issue 1, pp 151–160

# Partitions, sufficiency and undominated families of probability measures

• G. Trenkler
Article

## Summary

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.

## Keywords

Probability Measure Statistical Structure Statistical Decision Underlying Structure Invariance Principle

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