A festschrift for Herman Rubin by Dasgupta A. (ed.)

By Dasgupta A. (ed.)

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Marchand and W. E. 3. Some related work Interestingly, the dominance result in (iii) of the normal model MLE was previously established, in a diferent manner, by Casella and Strawderman (1981) (see also Section 6). As well, other dominating estimators here were provided numerically by Kempthorne (1988). For the multivariate version of Example 2: X ∼ Np (θ, Ip ); (p ≥ 1); with θ ≤ m, Marchand and Perron (2001) give dominating estimators of δmle (X) under squared error loss d−θ 2 . Namely, using a similar risk decomposition as above, including argument (ii), they show that δBU (X) (Bayes with respect to a boundary √ uniform prior) dominates δmle (X) whenever m ≤ p.

In Proc. Fourth Berkeley Symp. Math. Statist. Probab. 1, 361–380. Berkeley: University of California Press. MR133191 [15] Johnson, B. (1991). On the admissibility of improper Bayes inferences in fair Bayes decision problems. D. Thesis, University of Minnesota. [16] Johnstone, I. (1984). Admissibility, difference equations and recurrence in estimating a Poisson mean. Ann. Statist. 12, 1173–1198. MR760682 [17] Johnstone, I. (1986). Admissible estimation, Dirichlet principles, and recurp . Probab.

J. R. S. S. - B. 56, 543–548. MR1278226 [24] Srinivasan, C. (1981). Admissible generalized Bayes estimators and exterior boundary value problems. Sankhya Ser. A. 43, 1–25. MR656265 [25] Stein, C. (1955). A necessary and sufficient condition for admissibility. Ann. Math. Statist. 76, 518–522. MR70929 [26] Stein, C. (1959). The admissibility of Pitman’s estimator of a single location parameter. Ann. Math. , 30, 970–979. MR109392 [27] Zidek, J. V. (1970). Sufficient conditions for admissibility under squared error loss of formal Bayes estimators.

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