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September, 1963 Generalized Bayes Solutions in Estimation Problems
Jerome Sacks
Ann. Math. Statist. 34(3): 751-768 (September, 1963). DOI: 10.1214/aoms/1177704001


In estimation problems where the parameter space is not compact the class of Bayes solutions $(\mathscr{B})$ is usually not a complete class and it is necessary to take the closure (in a suitable sense) of $(\mathscr{B})$ to obtain a complete class. When the parameter to be estimated is that of an exponential density the limits of Bayes solutions can be characterized as generalized Bayes solutions in the sense that they minimize a posteriori risk where the a priori distribution may have infinite variation (theorem and corollaries in Section 2). The extent to which exponential densities are necessary for this characterization and some consequences of this characterization are contained in a series of remarks at the end of Section 2. In Section 1 we motivate the ideas by obtaining the above characterization for the problem of estimating the mean of a normal distribution with the parameter space restricted to $\lbrack0, \infty)$ and with squared-error loss function.


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Jerome Sacks. "Generalized Bayes Solutions in Estimation Problems." Ann. Math. Statist. 34 (3) 751 - 768, September, 1963.


Published: September, 1963
First available in Project Euclid: 27 April 2007

zbMATH: 0129.32402
MathSciNet: MR150908
Digital Object Identifier: 10.1214/aoms/1177704001

Rights: Copyright © 1963 Institute of Mathematical Statistics

Vol.34 • No. 3 • September, 1963
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