On derived estimators from the maximum likelihood estimator: minimaxity and improvement of the James-Stein estimator

  • Mekki Terbeche Mohamed Boudiaf, Laboratory\\ of Analysis and Application of Radiation (LAAR), Oran, USTO-MB,\\ Algeria
  • Abdenour Hamdaoui University of Sciences and Technologies of Oran, Mohamed Boudiaf, USTOMB
  • Abdelkader Benkhaled niversity of Mascara, \\Laboratory of Stochastic Models, Statistics and Applications, University Tahar Moulay of Sa\"{\i}da, Mascara, Algeria.
  • Ahmed Benmeftah University of Sciences and Technology, Mohamed Boudiaf,Oran, USTO-MB, Algeria.


The purpose of this study is the use of two general classes of shrinkage estimators for a multivariate normal mean. Under the balanced
loss function, we give sufficient conditions on the minimaxity of estimators of the first class and improve James-Stein estimator by
estimators of the second class. Then we deduce that both classes perform much better than the maximum likelihood estimator (MLE),
consequently the considered estimators are minimax. This approach is illustrated by simulation results.