Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Sequence of Improvement over the Lindley Type Estimator with the Cases of Unknown Covariance Matrices

  • Kim, Byung-Hwee (Department of Mathematics, Hanyang University) ;
  • Baek, Hoh-Yoo (Division of Mathematics and Informational Statistics, Wonkwang University)
  • Published : 2005.08.01
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Abstract

In this paper, the problem of estimating a p-variate (p $\ge$4) normal mean vector is considered in decision-theoretic set up. Using a simple property of the noncentral chi-square distribution, a sequence of estimators dominating the Lindley type estimator with the cases of unknown covariance matrices has been produced and each improved estimator is better than previous one.

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References

  1. Casella, G. and Berger, R. L. (1990). Statistical Inference, Brooks/Cole Publishing Company, Belmont, California
  2. Efron, B. and Morris, C. (1976). Families of Minimax Estimators of the Mean of a Multivariate Normal Distribution, The Annals of Statistics Vol. 4, NO.1, 11-21 https://doi.org/10.1214/aos/1176343344
  3. Ghosh, M., Hwang, J. T. and Tsui, K. K. (1984). Construction of improved estimators in multiparameter estimation for continuous exponential families, Journal of Multivariate Analysis 14, 212-220 https://doi.org/10.1016/0047-259X(84)90006-X
  4. Graybill, F. A. (1976). Theory and Application of the Linear Model, Duxbury Press
  5. Guo, T. and Pal, N. (1992). A sequence of improvements over the James-Stein Estimator, Journal of Multivariate Analysis 42, 302-317 https://doi.org/10.1016/0047-259X(92)90050-P
  6. James, W. and Stein, C. (1961). Estimation with quadratic loss, In Proceedings of the Fourth Berkely Symposium on Mathematics, Statistics and Probability 1, 361-380, Univ. of California Press, Berkeley
  7. Kubokawa, T. (1991). An Approach to Improving the James-Stein Estimator, Journal of Multivariate Analysis 36, 121-126 https://doi.org/10.1016/0047-259X(91)90096-K
  8. Lindley, D. V. (1962). Discussion of paper by C. Stein, Journal of Royal Statistical Society B24, 256-296
  9. Rao, C. R. (1983). Linear Statistical Inference and Its Application, Second Edition, John Wiley & Sons

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