Stein's positive part estimator and bayes estimator

  • Yoshikazu Takada


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.


Stein Multivariate Normal Distribution Balance Incomplete Block Design Posterior Mode Quadratic Loss Function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Efron, B. and Morris, C. (1973). Stein's estimation rules and its competitors—An empirical Bayes approach,J. Amer. Statist. Ass.,68, 117–130.MathSciNetzbMATHGoogle Scholar
  2. [2]
    James, W. and Stein, C. M. (1961). Estimation with quadratic loss function,Proc. 4th Berkeley Symp. Math. Statist. Prob.,1, 361–379.zbMATHGoogle Scholar
  3. [3]
    Lehmann, E. L. (1959).Testing Statistical Hypotheses, Wiley, New York.zbMATHGoogle Scholar
  4. [4]
    National Bureau of Standards, Applied Mathematics Series 55 (1964).Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables.Google Scholar
  5. [5]
    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.MathSciNetzbMATHGoogle Scholar
  6. [6]
    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.Google Scholar
  7. [7]
    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.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Strawderman, W. E. (1971). Proper Bayes minimax estimators of the multivariate normal mean,Ann. Math. Statist.,42, 385–388.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1979

Authors and Affiliations

  • Yoshikazu Takada
    • 1
  1. 1.University of TsukubaTsukubaJapan

Personalised recommendations