Journal article
Large covariance estimation by thresholding principal orthogonal complements
Journal of the Royal Statistical Society. Series B, Statistical methodology, Vol.75(4), pp.603-680
09/2013
DOI: 10.1111/rssb.12016
PMCID: PMC3859166
PMID: 24348088
Abstract
The paper deals with the estimation of a high dimensional covariance with a conditional sparsity structure and fast diverging eigenvalues. By assuming a 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 method POET' to explore such an approximate factor structure with sparsity. The POET-estimator includes the sample covariance matrix, the factor-based covariance matrix, the thresholding estimator and the adaptive thresholding estimator as specific 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. It is shown that the effect 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 verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.
Details
- Title: Subtitle
- Large covariance estimation by thresholding principal orthogonal complements
- Creators
- Jianqing Fan - Princeton UniversityYuan Liao - University of Maryland, College ParkMartina Mincheva - Princeton University
- Resource Type
- Journal article
- Publication Details
- Journal of the Royal Statistical Society. Series B, Statistical methodology, Vol.75(4), pp.603-680
- DOI
- 10.1111/rssb.12016
- PMID
- 24348088
- PMCID
- PMC3859166
- NLM abbreviation
- J R Stat Soc Series B Stat Methodol
- ISSN
- 1369-7412
- eISSN
- 1467-9868
- Publisher
- Oxford Univ Press
- Number of pages
- 78
- Grant note
- EP/J017213/1 / EPSRC; UK Research & Innovation (UKRI); Engineering & Physical Sciences Research Council (EPSRC) R01GM100474-01; R01-GM072611 / National Institutes of Health; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA Bendheim Center for Finance at Princeton University
- Language
- English
- Date published
- 09/2013
- Academic Unit
- Economics
- Record Identifier
- 9984936841802771
Metrics
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