Error covariance matrix estimation using ridge estimator

This article considers sparse covariance matrix estimation of high dimension. In contrast to the existing methods which are based on the residual estimation from least squares estimator, we utilize residuals from ridge estimator with the adaptive thresholding technique to estimate the error covariance matrix in high dimensional factor model. By obtaining the explicit convergence rates of the ridge estimator under regularity conditions, we formulated our thresholding estimator of the true covariance matrix. Our thresholding estimator can be applied to more scenarios and is shown to have comparable rate of convergence to Fan et al. (2011).