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Heuristic Procedures for Simultaneous Estimation of Several Normal Means

Published online by Cambridge University Press:  27 July 2009

Chi-Hyuck Jun
Chi-Hyuck Jun
Affiliation:
Department ofIndustrial Engineering Pohang Institute of Science and Technology (POS TECH) Pohang, Korea
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Abstract

Simultaneous estimation problems that deal with the estimation of several means for normal distributions are considered under the squared-error loss. Heuristic procedures are presented which can be applied to parameter estimation problems for a wide class of distributions specified only by their means and variances. Explicit results are obtained for the heuristic shrinkage estimators in the normal distribution case. Limiting behavior of the relative risk savings of these estimators is studied. The performances of the proposed estimators for normal distribution means are compared with other existing estimators by a computer simulation.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 1 , January 1988 , pp. 95 - 113
Copyright
Copyright © Cambridge University Press 1988

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References

Baranchik, A.J. (1970). A family of minimax estimators of the mean of a multivariate normal distribution. The Annals of Mathematical Statistics 41(2): 642–645.CrossRefGoogle Scholar
Berger, J.O. (1975). Minimax estimation of location vectors for a wide class of densities. Annals of Statistics 3: 1318–1328.CrossRefGoogle Scholar
Berger, J.O. (1980). A robust generalized Bayes estimator and confidence region for a multivariate normal mean. The Annals of statistics 8(4): 716–761.CrossRefGoogle Scholar
Berger, J.O. & Dey, D.K. (1983). Combining coordinates in simultaneous estimation of normal means. Journal of Statistical Planning and Inference 8: 143–160.CrossRefGoogle Scholar
Brown, L.D. (1966). On the admissibility of invariant estimators of one or more location parameters. Annals of Mathematical Statistics 37(5): 1087–1136.CrossRefGoogle Scholar
Casella, G. & Hwang, J.T. (1982). Limit expressions for the risk of James–Stein estimators. The Canadian Journal of Statistics 10(4): 305–309.CrossRefGoogle Scholar
Efron, B. & Morris, C. (1973). Stein's estimation rule and its competitors–An empirical Bayes approach. Journal of the American Statistical Association, Theory & Methods Section. 68(341):117–130.Google Scholar
Efron, B. & Morris, C. (1976). Families of minimax estimators of the mean of a multivariate normal distribution. The Annals of Statistics 4: 11–21.CrossRefGoogle Scholar
Hudson, H.M. (1978). A natural identity for exponential families with applications in multiparameter estimation. The Annals of Statistics 6(3): 473–484.CrossRefGoogle Scholar
James, W. & Stein, C. (1961). Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability I: 361–379.Google Scholar
Jun, C.-H. (1986). Heuristic procedures of simultaneous estimation of several means. Ph.D. thesis, University of California, Berkeley.Google Scholar
Law, A.M. & Kelton, W.D. (1982). Simulation modeling and analysis. New York:McGraw-Hill.Google Scholar
Lindley, D.V. (1962). Discussion on Professor Stein's paper. Journal of the Royal Statistical Society, Series B, 24: 285–287.Google Scholar
Morris, C. (1983). Parametric empirical Bayes inference: Theory and applications. Journal of the American Statistical Association, Application Section. 78 (381): 47–65.CrossRefGoogle Scholar
Robbins, H. (1983). Some thoughts on empirical Bayes estimation. The Annals of Statistics 11(3): 713–723.CrossRefGoogle Scholar
Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability 1: 197–206.Google Scholar
Stein, C. (1981). Estimation of the mean of a multivariate normal distribution. The Annals of Statistics 9(6): 1135–1151.CrossRefGoogle Scholar
Tsui, K-W. & Press, S.J. (1982). Simultaneous estimation of several Poisson parameters under k−normalized squared-error loss. The Annals of Statistics 10(1): 93–100.CrossRefGoogle Scholar