Large covariance estimation by thresholding principal orthogonal complements

Jianqing Fan, Yuan Liao and Martina Mincheva

MPRA Paper from University Library of Munich, Germany

Abstract: This paper deals with estimation of high-dimensional covariance with a conditional sparsity structure, which is the composition of a low-rank matrix plus a sparse matrix. By assuming sparse error covariance matrix in a multi-factor model, we allow the presence of the 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. 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 specic examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms, including the spectral norm. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also veried by extensive simulation studies.

Keywords: High dimensionality; approximate factor model; unknown factors; principal components; sparse matrix; low-rank matrix; thresholding; cross-sectional correlation (search for similar items in EconPapers)
JEL-codes: C01 C13 (search for similar items in EconPapers)
Date: 2011
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (30)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/38697/1/MPRA_paper_38697.pdf original version (application/pdf)

Related works:
Journal Article: Large covariance estimation by thresholding principal orthogonal complements (2013)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:38697

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().