On unbiased and improved loss estimation for the mean of a multivariate normal distribution with unknown variance

Journal of Statistical Planning and Inference

Volumn 119, Issue 1, 2004, Pages 17-22

  Wan, Alan T K ^a   Zou, Guohua ^b,c  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b INSTITUTE OF SYSTEMS SCIENCE   (China)

^c YALE UNIVERSITY   (United States)

Author keywords

James Stein estimator; Positive part rule; Quadratic loss; Risk

Indexed keywords

EID: 0242551125     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(02)00406-8     Document Type: Article

References (13)

1. Efron B.F. Morris C.N. Stein's estimation rule and its competitors-an empirical Bayes approach J. Amer. Statist. Assoc. 68 1973 117-130
2. James, W., Stein, C., 1961. Estimation with quadratic loss. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley, pp. 361-380.
3. Johnstone, I.M., 1988. On inadmissibility of some unbiased estimates of loss. In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics, Vol. IV. Springer, New York, pp. 361-379.
4. Kiefer J. Admissibility conditional confidence procedures Ann. Statist. 4 1976 836-865
5. Lele C. Inadmissibility of loss estimators Statist. Decisions 10 1992 309-322
6. Lu K.L. Berger J.O. Estimation of normal means: frequentist estimation of loss Ann. Statist. 17 1989 890-906
7. Rukhin, A.L., 1988. Estimated loss and admissible loss estimators. In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics, Vol. IV, Springer, New York, pp. 409-418.
8. Rukhin A.L. Estimating the loss of estimators of a binomial parameter Biometrika 75 1988 153-155
9. Rukhin A.L. Loss functions for loss estimation Ann. Statist. 16 1988 1262-1269
10. Sandved E. Ancillary statistics and estimation of the loss in estimation problems Ann. Math. Statist. 39 1968 1755-1758
11. Stein, C., 1956. Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley, pp. 197-206.
12. Wan, A.T.K., Zou, G., 2002. On estimating the losses of improved estimators. Unpublished Technical Report, Department of Management Sciences, City University of Hong Kong.
13. Zou G. Admissible estimation of vector loss and matrix loss J. Eng. Math. 12 1995 17-26 (in Chinese)