Summary
Stein's positive part estimator forp normal means is known to dominate the M.L.E. ifp≧3. In this article by introducing some proirs we show that Stein's positive part estimator is posterior mode. We also consider the Bayes estimators (posterior mean) with respect to the same priors and show that some of them dominate M.L.E. and are admissible.
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References
Efron, B. and Morris, C. (1973). Stein's estimation rules and its competitors—An empirical Bayes approach,J. Amer. Statist. Ass.,68, 117–130.
James, W. and Stein, C. M. (1961). Estimation with quadratic loss function,Proc. 4th Berkeley Symp. Math. Statist. Prob.,1, 361–379.
Lehmann, E. L. (1959).Testing Statistical Hypotheses, Wiley, New York.
National Bureau of Standards, Applied Mathematics Series 55 (1964).Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables.
Stein, C. M. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution,Proc. 3rd Berkeley Symp. Math. Statist. Prob.,1, 197–206.
Stein, C. M. (1966). An approach to the recovery of inter-block information in balanced incomplete block designs, In Festschrift for J. Neyman:Research Papers in Statistics (ed. F. N. David), Wiley, New York, 351–366.
Strawderman, W. E. and Cohen, A. (1971). Admissibility of estimators of the mean vector of a multivariate normal distribution with quardratic loss,Ann. Math. Statist.,42, 270–296.
Strawderman, W. E. (1971). Proper Bayes minimax estimators of the multivariate normal mean,Ann. Math. Statist.,42, 385–388.
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Takada, Y. Stein's positive part estimator and bayes estimator. Ann Inst Stat Math 31, 177–183 (1979). https://doi.org/10.1007/BF02480275
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DOI: https://doi.org/10.1007/BF02480275