1. g2-minimax estimators in the exponential family
- Author
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J. J. Deely, W. J. Zimmer, T. M. O'donovan, and D. A. Jackson
- Subjects
Statistics and Probability ,Statistics::Theory ,Applied Mathematics ,General Mathematics ,Estimator ,U-statistic ,Agricultural and Biological Sciences (miscellaneous) ,Lehmann–Scheffé theorem ,Minimum-variance unbiased estimator ,Exponential family ,Efficient estimator ,Stein's unbiased risk estimate ,Statistics ,Applied mathematics ,Statistics, Probability and Uncertainty ,General Agricultural and Biological Sciences ,Completeness (statistics) ,Mathematics - Abstract
SUMMARY It is shown that, for quadratic loss and members of the exponential family with an unbiased sufficient statistic having a variance which is quadratic in the parameter, a C2-minimax estimator exists. In addition, the estimator is of simple form and appears to satisfy intuition. Also, it is shown that the 62-minimax estimator is admissible in the usual sense, is 92-admissible and makes the unbiased sufficient statistic inadmissible in S2. Finally, in this situation, the natural conjugate prior distribution is always a member of the Pearson family and is always least favourable. Asymptotic 92-minimax estimators are discussed briefly.
- Published
- 1970
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