Nonparametric Shrinkage Estimator for Covariance Matrix Under Heterogeneity and High Dimensions Conditions

In this paper, we discuss different kinds of covariance matrix estimators and their behavior under the conditions of heterogeneity and high dimensions. Covariance matrix estimation that is well-conditioned matrix is very important procedure for many statistical applications which require that. Sometimes, the common estimator of covariance matrix - the sample covariance matrix- suffers from ill conditions and in many cases be invertible and without good qualities of estimator as dimensions of matrix go larger. Here, we view a shrinkage estimator for covariance matrix which is a combination of unbiased estimator and minimum variance estimator with different types of shrinkage factors parametric and non-parametric ones. Simulation study have been made by using Heterogeneous Autoregressive Process ARH(1) as a structure covariance matrix for population, moreover, a comparison has been made among different types of covariance estimators by using minimum mean square errors MMSE.