An Improvement of the James-Stein Estimator with Some Shrinkage Points using the Stein Variance Estimator

Title & Authors
An Improvement of the James-Stein Estimator with Some Shrinkage Points using the Stein Variance Estimator
Lee, Ki Won; Baek, Hoh Yoo;

Abstract
Consider a p-variate($\small{p{\geq}3}$) normal distribution with mean $\small{{\theta}}$ and covariance matrix $\small{{\sum}={\sigma}^2{\mathbf{I}}_p}$ for any unknown scalar $\small{{\sigma}^2}$. In this paper we improve the James-Stein estimator of $\small{{\theta}}$ in cases of shrinking toward some vectors using the Stein variance estimator. It is also shown that this domination does not hold for the positive part versions of these estimators.
Keywords
Shrinkage points;James-Stein estimator;Stein variance estimator;domination;
Language
English
Cited by
References
1.
Abramowitz, M. and Stegun, I. A. (1964). Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards Applied Mathematics Series 55, U.S..

2.
Baek, H. Y. and Han, K. H. (2004). Some sequences of improvement over Lindley type estimator, Honam Mathematical Journal, 26, 219-236.

3.
Baranchik, A. J. (1970). A family of minimax estimators of a multivariate normal distribution, Annals of Mathematical Statistics, 41, 642-645.

4.
Berry, J. C. (1994). Improving the James-Stein estimator using the Stein variance estimator, Statistics and Probability Letters, 20, 241-245.

5.
George, E. I. (1990). Comment on "Decision theoretic variance estimation", by Maatta and Casella, Statistical Science, 5, 107-109.

6.
James, W. and Stein, C. (1961). Estimation with quadratic loss, Proceedings of the fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, 361-379.

7.
Kim, B. H., Baek, H. Y. and Chang, I. H. (2002). Improved estimators of the natural parameters in continuous multiparameter exponential families, Communications in Statistics-Theory and Methods, 31, 11-29.

8.
Kim, B. H., Koh, T. W. and Baek, H. Y. (1995). Estimators with nondecreasing risk in a multivariate normal distribution, Journal of the Korean Statistical Society, 24, 257-266.

9.
Lehmann, E. L. and Casella, G. (1999). Theory of Point Estimation, 2nd ed., Springer-Verlag, New York.

10.
Lindley, D. V. (1962). Discussion of Paper by C. Stein, Journal of the Royal Statistical Society, Series B, 24, 265-296.

11.
Maruyama, Y. (1996). Estimation of the mean vector and the variance of a multivariate normal distribution, Master Thesis of Graduate School of Economics, University of Tokyo.

12.
Park, T. R. and Baek, H. Y. (2011). An approach to improving the Lindley estimator, Journal of the Korean Data & Information Science Society, 22, 1251-1256.

13.
Stein, C. (1964). Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean, Annals of the Institute of Statistical Mathematics, 16, 155-160.

14.
Stein, C. (1981). Estimation of the mean of a multivariate normal distribution, The Annals of Statistics, 9, 1135-1151.

15.
Strawderman, W. (1973). Proper Bayes minimax estimators of the multivariate normal mean vector for common unknown variance, Annals of Mathematical Statistics, 6, 1189-1194.