التقدير المقلص الحصين واللاخطي لمصفوفة التباين والتباين المشترك ذات الابعاد الكبيرة بوجود مشكلة الارتباط الذاتي

Abstract

When the dimensions of the covariance matrix are relatively large compared with the sample size ; or when the dimensions of the matrix are close to the sample size , There will be difficulties in finding a good estimation for it. Most Matrices with high dimension suffer from the difficulty of finding their inverse. Therefore, the classical methods of estimation such as maximum likelihood will give biased estimators and far from their true value. This research aims at expanding usage of shrinkage estimation to estimate the covariance matrix in the case of using samples with large dimensions.The covariance matrix will be estimated by using Two methods. The robust shrinkage estimator Chen and the nonlinear shrinkage estimator Oracle, and make comparison among them based on (MMSE) minimum mean square errors. Here, a simulated experiment with high dimensions samples was made with multiple sizes and calculated MMSE as the increasing in sample size to the large dimension of covariance matrix