On partial sufficiency: A review |
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Authors: | D Basu |
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Affiliation: | The Florida State University, Tallahassee, Fl, U.S.A. |
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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). |
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Keywords: | 60A05 62A15 Ancillary statistics information nuisance parameters specific sufficiency θ-oriented statistics |
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