A new approach for ultrahigh-dimensional covariance matrix estimation

Abstract

We propose a method for estimating ultrahigh dimensional covariance matrix without the Gaussian distribution and the order of variables assumptions. More specifically, by combining the modified Cholesky decomposition (MCD) and refitted cross validation (RCV), a permutation invariant method called CovPRCV is developed to estimate covariance matrix under the “Permutation-Average” framework. The employment of RCV procedure attenuates significantly spurious correlation in the ultrahigh dimensional data. We derive the consistency of proposed estimator under the Frobenius norm without requiring banded structure and normal distribution. The finite-sample performance is assessed via simulation studies, which indicate that the proposed method is promising compared with its competitors in many interesting scenarios. We also apply the proposed method to analyze a prostate dataset.