Abstract
In this paper the concept of statistical sufficiency is studied within a general probability setting. It is not assumed that the family of probability measures is dominated. That is, it is not assumed that there is a σ-finite measure μ such that each probability measure in the family is absolutely continuous with respect to μ. In the dominated case, the theory of sufficiency has received a thorough-going and elegant treatment by Halmos and Savage [6], Bahadur [2], and others. Although many families of probability measures of importance for statistical work are dominated, many others are not. Nonparametric statistical work, especially, abounds with undominated families. It seems appropriate, therefore, to see what can be learned about sufficiency in the undominated case.
Received September 9, 1960.
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References
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Davis, B., Song, R. (2011). Sufficiency in the Undominated Case. In: Davis, B., Song, R. (eds) Selected Works of Donald L. Burkholder. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7245-3_4
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DOI: https://doi.org/10.1007/978-1-4419-7245-3_4
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