Minimaxity of empirical bayes estimators shrinking toward the grand mean when variances are unequal

Communications in Statistics - Theory and Methods

Volumn 25, Issue 1, 1996, Pages 183-199

  Shinozaki, Nobuo ^a   Chang, Yuan Tsung ^b  

^a KEIO UNIVERSITY   (Japan)

^b MEJIRO UNIVERSITY   (Japan)

Author keywords

Regression estimate; Squared error loss function; Stein estimator; Uniform improvement

Indexed keywords

EID: 0346503188     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1080/03610929608831687     Document Type: Article

References (11)

1. Berger,J.O.(1978). "Minimax estimation of a multivariate normal mean under polynomial loss", J. Multivariate Anal., 8, 173-180.
2. Berger,J.O.(1985). Statistical Decision Theory and Bayesian Analysis, 2nd ed., Springer, New York.
3. Berger,J.O. and Robert,C.(1990). "Subjective hierarchical Bayes estimation of a multivariate normal mean : On the frequentist interface", Ann. Statist., 18, 617-651.
4. Carter,G.M. and Rolph,J.E.(1974). "Empirical Bayes methods applied to estimating fire alarm probabilities", J. Amer. Statist. Assoc., 69, 880-885.
5. Efron,B and Morris,C(1972). "Limiting the risk of Bayes and empirical Bayes estimators- Part II : The empirical Bayes case", J. Amer. Statist. Assoc., 67, 130-139.
6. Efron,B and Morris,C(1973). "Stein's estimation rule and its competitors - an empirical Bayes approach", J. Amer. Statist. Assoc., 68, 117-130.
7. Fay,R.E.III and Herriot,R.A.(1979). "Estimates of income for small places: An application of James-Stein procedures to census data", J. Amer. Statist. Assoc., 74, 269-277.
8. James,W. and Stein,C.(1961). "Estimation with quadratic loss", Proc. Fourth Berkeley Symp. Math. Statist. Prob., 1, 361-380. Univ. California Press.
9. Morris,C.(1983). "Parametric empirical Bayes inference: Theory and applications", J. Amer. Statist. Assoc., 78, 47-65.
10. Prasad,N.G.N. and Rao,J.N.K.(1990). "The estimation of the mean squared error of small-area estimators", J. Amer. Statist. Assoc., 85, 163-171.
11. Shinozaki,N. and Chang,Y.T.(1993). "Minimaxity of empirical Bayes estimators of the means of independent normal variables with unequal variances", Comm. Statist. - Theory Meth., 22(8), 2147-2169.