A Unified and Broadened Class of Admissible Minimax Estimators of a Multivariate Normal Mean

Journal of Multivariate Analysis

Volumn 64, Issue 2, 1998, Pages 196-205

  Maruyama, Yuzo ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Admissible, minimax, multivariate normal mean, generalized Bayes, quadratic loss

Indexed keywords

EID: 0012535360     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1997.1715     Document Type: Article

References (15)

1. Abramowitz, M. Stegun, I. A. 1964, Handbook of Mathematical Functions, Dover, New York.
2. Alam K. A family of admissible minimax estimators of the mean of a multivariate normal distribution. Ann. Statist. 1:1973;517-525.
3. Baranchik A. J. Multiple regression and estimation of the mean of a multivariate normal distribution. Tech. Rep. 1964;Stanford University.
4. Baranchik A. J. A family of minimax estimators of the mean of a multivariate normal distribution. Ann. Math. Statist. 41:1970;642-645.
5. Berger J. Admissible minimax estimation of multivariate normal mean with arbitrary quadratic loss. Ann. Statist. 4:1976;223-226.
6. Brown L. D. Admissible estimators, recurrent diffusions, and insoluble boundary value problems. Ann. Math. Statist. 42:1971;855-903.
7. DasGupta A., Strawderman W. E. All estimates with a given risk, Riccati differential equations and a new proof of a theorem of Brown. Ann. Statist. 25:1997;1208-1221.
8. Efron B., Morris C. Families of minimax estimators of the mean of a multivariate normal distribution. Ann. Statist. 4:1976;11-21.
9. Faith R. E. Minimax Bayes estimators of a multivariate normal mean. J. Multivariate Anal. 8:1978;372-379.
10. James W., Stein C. Estimation of quadratic loss. Proc. 4th Berkeley Symposium on Mathematical Statistics and Probability. 1961;Univ. of California Press, Berkeley. p. 361-379.
11. Lehmann E. L. Testing Statistical Hypotheses. 1986;Wiley, New York.
12. Stein C. Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proc. 3rd Berkeley Symposium on Mathematical Statistics and Probability. 1956;Univ. of California Press, Berkeley. p. 197-206.
13. Stein C. Estimation of the mean of a multivariate normal distribution. Proc. Prague Symposium Asymptotic Statistics. 1973;. p. 345-381.
14. Strawderman W. E. Proper Bayes minimax estimators of multivariate normal mean. Ann. Statist. 42:1971;385-388.
15. Takada Y. Stein's positive part estimator and Bayes estimators. Ann. Inst. Statist. Math. 31:1979;177-183.