High-dimensional covariance matrix estimation under the SSE model (New Developments in Statistical Model)

Abstract

In this paper, we consider the estimation for the inverse matrix of a high-dimensional covariance matrix under the strongly spiked eigenvalue model. One of the well-known estimation methods is the principal orthogonal complement thresholding (POET) given by Fan et al. [5]. We show that the POET has consistency properties only under several severe conditions in high-dimensional settings. In order to overcome the difficulty, we consider applying the noise-reduction (NR) method given by Yata and Aoshima [8, 9] to the POET. We propose a new estimation of the inverse covariance matrix called the NR-POET. We compare the performance of the NR-POET with the POET by several simulations.