Abstract
The notion of a sufficient statistic—a statistic that summarizes in itself all the relevant information. in the sample x about the universal parameter ω—is acclaimed as one of the most significant discoveries of Sir Ronald A. Fisher. It is however not well-recognized that the related notion of a partially sufficient statistic—a statistic that isolates and exhausts all the relevant and usable information in the sample about a sub-parameter θ = θ(ω)—can be very elusive if the question is posed in sample space terms. In this review article, the author tries to unravel the mystery that surrounds the notion of partial sufficiency. For mathematical details on some of the issues raised here one may refer to Basu ;1977).
*Based on an invited talk given by the author at the August, 1976 annual meeting of the Institute of Mathematical Statistics.
**Partially supported by NSF research grant no. MCS77 01661.
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Acknowledgment
The author wishes to thank Professor Oscar Kempthorne for carefully going over an earlier draft of the paper.
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Basu**, D. (2011). On Partial Sufficiency: A Review*. In: DasGupta, A. (eds) Selected Works of Debabrata Basu. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5825-9_27
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