COMPARISON MRCD AND ORACLE FOR ESTIMATING THE DETERMINANT OF HIGH DIMENSIONAL COVARIANCE MATRIX

Abstract

Estimating the variance matrix has an important role in statistical applications and conclusions, in high–dimensional matrices if the number of variables is greater than the number of observations P > n, the traditional statistical methods are not reliable because they give uncontrolled estimates. Shrinkage methods are used to estimate the high–dimensional variance matrix. In this research, the high–dimensional variance matrix was estimated using the robust Nonparametric method Minimum Regularized Covariance Determinant (MRCD), which is based on Mahalanobis distance, and compared with the variance matrix estimated by the Oracle method, which is based on the Frobenius criterion