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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bahadur, R. R. (1954). Sufficiency and statistical decision functions,Ann. Math. Statist.,25, 423–462.
Basu, D. (1970). On sufficiency and invariance,Essays in Probability and Statistics, Univ. of North Carolina Press, Chapel Hill, N.C.
Basu, D. and Ghosh, J. K. (1969). Sufficient statistics in sampling from a finite universe,Proc. 36th Session Internat. Statist. Inst., 850–859.
Blackwell, D. and Girshick, A. A. (1954).Theory of Games and Statistical Decisions, Wiley, New York.
Burkholder, D. L. (1961). Sufficiency in the undominated case,Ann. Math. Statist.,32, 1191–1200.
Hasegawa, M. and Perlman, M. D. (1974). On the existence of a minimal sufficient subfield,Ann. Statist.,2, 1049–1055.
Morimoto, H. (1972). Statistical structure of the problem of sampling from finite populations,Ann. Math. Statist.,43, 490–497.
Author information
Authors and Affiliations
About this article
Cite this article
Trenkler, G. Partitions, sufficiency and undominated families of probability measures. Ann Inst Stat Math 34, 151–160 (1982). https://doi.org/10.1007/BF02481017
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02481017