Development of a reduced estimator to estimate the variance and covariance matrix with large dimensions using hyperbolic trigonometric functions - (Chemical properties of the soil of the Tigris Basin in Wasit Governorate)
Keywords:
covariance matrix using hyperbolic trigonometric functions, Large-dimensional varianceAbstract
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 or larger, 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 three methods. The Maximum Likelihood estimator MLE and the nonlinear shrinkage estimator Oracle, and the linear shrinkage estimator Lediot and Wolf (LW) and the Suggested Estimator 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.
As conclusions, the Suggested Estimator is perfect when the sample size is very small compared with the number of variables in it. Moreover, the Oracle estimator is working well when the sample size is fairly small to the number of variables in it while it has not cleared that the maximum likelihood estimator MLE and the (LW) have any goodness.
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