A new class of generalized bayes minimax ridge regression estimators

Annals of Statistics

Volumn 33, Issue 4, 2005, Pages 1753-1770

  Maruyama, Yuzo ^a   Strawderman, William E ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Condition number; Generalized bayes; Minimaxity; Ridge regression

Indexed keywords

EID: 26444582265     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000327     Document Type: Article

References (19)

1. BARANCHIK, A. J. (1970). A family of minimax estimators of the mean of a multivariate normal distribution. Ann. Math. Statist. 41 642-645.
2. BELSLEY, D. A., KUH, E. and WELSCH, R. E. (1980). Regression Diagnostics. Wiley, New York.
3. BERGER, J. (1976). Admissible minimax estimation of a multivariate normal mean with arbitrary quadratic loss. Ann. Statist. 4 223-226.
4. BERGER, J. (1980). A robust generalized Bayes estimator and confidence region for a multivariate normal mean. Ann. Statist. 8 716-761.
5. BERGER, J. and SRINIVASAN, C. (1978). Generalized Bayes estimators in multivariate problems. Ann. Statist. 6 783-801.
6. BOCK, M. E. (1975). Minimax estimators of the mean of a multivariate normal distribution. Ann. Statist. 3 209-218.
7. CASELLA, G. (1980). Minimax ridge regression estimation. Ann. Statist. 8 1036-1056.
8. CASELLA, G. (1985). Condition numbers and minimax ridge regression estimators. J. Amer. Statist. Assoc. 80 753-758.
9. EFRON, B. and MORRIS, C. (1976). Families of minimax estimators of the mean of a multivariate normal distribution. Ann. Statist. 4 11-21.
10. FAITH, R. E. (1978). Minimax Bayes estimators of a multivariate normal mean. J. Multivariate Anal. 8 372-379.
11. HOERL, A. E. and KENNARD, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12 55-67.
12. JAMES, W. and STEIN, C. (1961). Estimation with quadratic loss. Proc. Fourth Berkeley Symp. Math. Statist. Probab. 1 361-379. Univ. California Press, Berkeley.
13. KUBOKAWA, T. and SRIVASTAVA, M. S. (2001). Robust improvement in estimation of a mean matrix in an elliptically contoured distribution. J. Multivariate Anal. 76 138-152.
14. LIN, p. and TSAI, H. (1973). Generalized Bayes minimax estimators of the multivariate normal mean with unknown covariance matrix. Ann. Statist. 1 142-145.
15. MARUYAMA, Y. (2003). A robust generalized Bayes estimator improving on the James-Stein estimator for spherically symmetric distributions. Statist. Decisions 21 69-77.
16. ROBERT, C. (1994). The Bayesian Choice. Springer, New York.
17. STEIN, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proc. Third Berkeley Symp. Math. Statist. Probab. 1 197-206. Univ. California Press, Berkeley.
18. STRAWDERMAN, W. E. (1971). Proper Bayes minimax estimators of the multivariate normal mean. Ann. Math. Statist. 42 385-388.
19. STRAWDERMAN, W. E. (1978). Minimax adaptive generalized ridge regression estimators. J. Amer. Statist. Assoc. 73 623-627.