By Anirban Dasgupta
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Additional info for A Festschrift for Herman Rubin (Institute of Mathematical Statistics, Lecture Notes-Monograph Series)
Sankhya Ser. A. 43, 1–25. MR656265  Stein, C. (1955). A necessary and sufficient condition for admissibility. Ann. Math. Statist. 76, 518–522. MR70929  Stein, C. (1959). The admissibility of Pitman’s estimator of a single location parameter. Ann. Math. , 30, 970–979. MR109392  Zidek, J. V. (1970). Sufficient conditions for admissibility under squared error loss of formal Bayes estimators. Ann. Math. Statist. 41, 446–456. MR261742 A Festschrift for Herman Rubin Institute of Mathematical Statistics Lecture Notes – Monograph Series Vol.
An interesting and important issue to which we will not devote much effort is the amount of (relative or absolute) improvement in risk obtained by using procedures which take the restrictions on the parameter space into account. In certain situations the improvement is substantial. 5, so there is a 50% savings in risk (at θ = 0). Interestingly, at θ = 0, the risk of the Bayes estimator corresponding to the uniform prior on [0, ∞) is equal to the risk of the MLE so there is no savings in risk at θ = 0.
The right hand side of this inequality converges to zero as i −→ ∞. Hence H(C) = 0. Since C was an arbitrary λ-proper set, the chain W is locally-ν-recurrent. Acknowledgment Many thanks to Jim Hobert, Tiefeng Jiang and Galin Jones for their valuable comments. Also special thanks to Anirban Das Gupta for his efforts on this Festschrift for Herman Rubin and his many comments on this contribution. References  Blackwell, D. (1951). On the translation parameter problem for discrete variables. Ann.
A Festschrift for Herman Rubin (Institute of Mathematical Statistics, Lecture Notes-Monograph Series) by Anirban Dasgupta