19
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Robustness of the posterior mean in normal hierarchical models

&
Pages 1999-2014 | Received 01 Jul 1992, Published online: 23 Dec 2010

References

  • Berger , J. 1976 . Minimax estimation of a multivariate normal mean under arbitrary quadratic loss . J. Multivariate Anal , 6 : 256 – 264 .
  • Berger , J. 1980 . A robust generalized Bayes estimator and confidence region for a multivariate normal mean . Ann. Statist. , 8 : 716 – 761 .
  • Berger , J. 1982 . Bayesian robustness and the Stein effect . J. Amer. Statist. Assoc , 77 : 358 – 368 .
  • Berger , J. 1982 . Selecting a minimax estimator of a multivariate normal mean . Ann. Statist , 10 : 81 – 92 .
  • Berger , J. 1985 . Statistical Decision Theory and Bayesian Analysis , New York : Springer .
  • Berger , J. 1990 . Robust Bayesian analysis: sensitivity to the prior . J. Statist. Plann. Inference , 25 : 303 – 328 .
  • Berger , J. and Berliner , L.M. 1986 . Robust Bayes and empirical Bayes analysis with ε-contaminated priors . Ann. Statist , 14 : 461 – 486 .
  • Berger , J. and Chen , S.Y. 1987 . “ Minimaxity of empirical Bayes estimators derived from subjective hyperpriors ” . In Advances in Multivariate Statistical Analysis , Edited by: Gupta , A. K. 1 – 12 . D. Reidel Publishing Company .
  • Berger , J. and Robert , C. 1988 . “ Subjective hierarchical Bayes estimation of a multivariate normal mean: on the frequentist interface ” . In Technical Report #88-24C , Purdue University . Department of Statistics
  • DeRobertis , L. and Hartigan , J. A. 1981 . Bayesian inference using intervals of measures . Ann. Statist , 9 : 235 – 244 .
  • Edwards , W. , Lindman , H. and Savage , L.J. 1963 . Bayesian statistical inference for psychological research . Psychol. Rev , 70 ( 3 ) : 193 – 242 .
  • James , W. and Stein , C. 1961 . Estimation with quadratic loss. Proc. Fourth Berkeley Symp. Math. Statist. Probab , Vol. 1 , 361 – 379 . Univ. California Press .
  • Lu , K.L. and Berger , J. 1989 . Estimation of normal means: frequentist estimation of loss . Ann. Statist , 17 : 890 – 906 .
  • Moreno , E. and Cano , J.A. 1991 . Robust Bayesian analysis with e-contaminations partially known . J. Roy. Statist. Soc. Ser.B , 53 ( 1 ) : 143 – 155 .
  • Moreno , E. and Pericchi , L.R. 1988 . “ Robust Bayesian analysis for e-contaminations with shape and quantile constraints ” . In Technical Report , University of Granada .
  • Moreno , E. and Pericchi , L.R. 1990 . “ A Robust Bayesian elimination of hyperparameters ” . In Technical Report , University of Granada .
  • Stein , C. 1955 . “ Inadmissibility of the usual estimator for the mean of a multivariate normal distribution ” . In Proc. Third Berkeley Symp. Math. Statist. Probab , Vol. 1 , 197 – 206 . Univ. California Press .
  • Sivaganesan , S. and Berger , J. 1989 . Ranges of posterior measures for priors with unimodal contaminations . Ann. Statist , 17 : 868 – 889 .
  • Walley , P. and Pericchi , L.R. 1988 . Credible intervals; how credible they are. Technical Report , University Simon Bolivar .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.