Large Covariance Estimation by Thresholding Principal Orthogonal Complements

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific…

• PU
  Princeton University
• NI
  National Institutes of Health

  Awards: R01GM100474-01, DMS-0704337, R01-GM072611, R01GM100474
• EA
  Engineering and Physical Sciences Research Council

  Award: EP/J017213/1