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Abstract

In this paper, we are interested in estimating a multivariate normal mean under the balanced loss function using the shrinkage estimators deduced from the Maximum Likelihood Estimator (MLE). First, we consider a class of estimators containing the James-Stein estimator, we then show that any estimator of this class dominates the MLE, consequently it is minimax. Secondly, we deal with shrinkage estimators which are not only minimax but also dominate the James- Stein estimator.

Keywords

Balanced loss function James-Stein estimator minimax estimator non-central chi-square distribution shrinkage estimators

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How to Cite
Hamdaoui, A., Terbeche, M., & Benkhaled, A. (2021). On shrinkage estimators improving the James-Stein estimator under balanced loss function. Pakistan Journal of Statistics and Operation Research, 17(3), 711-727. https://doi.org/10.18187/pjsor.v17i3.3663
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References

  1. Amin, M., Nauman, A. M., and Amanullah, M. (2020). On the james-stein estimator for the poisson regression model. Comm. Statist. Simulation Comput., pages 1-14, doi.org/10.1080/03610918.2020.1775851.
  2. Arnold, F. S. (1981). The theory of Linear models and Multivariate analysis, pp. 9-10. John Wiley & Sons, New York, USA.
  3. Benkhaled, A. and Hamdaoui, A. (2019). General classes of shrinkage estimators for the multivariate normal mean with unknown variancee: Minimaxity and limit of risks ratios. Kragujevac J. Math., 46:193-213.
  4. Guikai, H., Qingguo, L., and Shenghua, L. (2014). Trisk comparison of improved estimators in a linear regression model with multivariate t errors under balanced loss function. Journal of Applied Mathematics, 354:1-7, doi.org/10.1155/2014/129205.
  5. Hamdaoui, A., Benkhaled, A., and Mezouar, N. (2020). Minimaxity and limits of risks ratios of shrink- age estimators of a multivariate normal mean in the bayesian case. Stat. Optim. Inf. Comput., 8:507-520, doi.org/10.19139/soic-2310-5070-735.
  6. Jafari, J., Leblan, A., and Marchand, E. (2014). On continuous distribution functions, minimax and bes invariant estimators and integrated balanced loss functions. Canad. J. Statistist., 42:470-486, doi.org/10.1002/cjs.11217.
  7. James, W. and Stein, C. (1961). Estimation with quadratic loss. Fourth Berkeley Symp. on Math. Statist. and Prob., Univ. of Calif. Press, Berkeley, 1:361-379.
  8. Karamikabir, H., Afsahri, M., and Arashi, M. (2018). Shrinkage estimation of non-negative mean vec- tor with unknown covariance under balance loss. Journal of Inequalities and Applications, pages 1-11, doi.org/10.1186/s13660-018-1919-0.
  9. Sanjari, F. and Asgharzadeh, A. (2004). Estimation of a normal mean relative to balanced loss functions. Statistical Papers, 45:279-286, doi.org/10.1007/BF02777228.
  10. Selahattin, K. and Issam, D. (2019). The optimal extended balanced loss function estimators. J. Comput. Appl. Math., 345:86-98, doi.org/10.1016/j.cam.2018.06.021.
  11. Selahattin, K., Sadullah, S., ozkale, M. R., and G ¨ uler, H. (2011). More on the restricted ridge regression ¨ estimation. J. Stat. Comput. Simul., 81:1433-1448, doi.org/10.1080/00949655.2010.491480.
  12. Stein, C. (1956). Inadmissibilty of the usual estimator for the mean of a multivariate normal distribution. Proc. 3th Berkeley Symp. on Math. Statist. and Prob., Univ. of Calif. Press, Berkeley, 1:197-206.
  13. Stein, C. (1981). Estimation of the mean of a multivariate normal distribution. International Statistical Review, 9:1135-1151, doi.org/10.1214/aos/1176345632.
  14. Tsukuma, H. and Kubukawa, T. (2015). Estimation of the mean vector in a singular multivariate normal distribution. J. Multivariate Anal., 140:215-232, doi.org/10.1016/j.jmva.2015.05.016.
  15. Xie, X., Kou, S. C., and Brown, B. (2016). Optimal shrinkage estimators of mean parameters in family of distribution with quadratic variance. Ann. Statist., 44:564-597, doi.org/10.1214/15-AOS1377.
  16. Yuzba, B., Arashi, M., and Ahmed, S. (2020). Shrinkage estimation strategies in generalised ridge regression models: Low/high-dimension regime. pages 1-23, doi.org/10.1111/insr.12351. Int. Stat. Rev.
  17. Zellner, A. (1994). Bayesian and non-bayesian estimation using balanced loss functions. Statistical Decision Theory and Related Topics, 8:337-390.
  18. Zinodiny, S., Leblan, S., and Nadarajah, S. (2017). Bayes minimax estimation of the mean matrix of matrix-variate normal distribution under balanced loss function. Statist. Probab. Lett., 125:110-120, doi.org/10.1016/j.spl.2017.02.003.