ArticleJournal of the Royal Statistical Society. Series B, Statistical methodology2013
Large Covariance Estimation by Thresholding Principal Orthogonal Complements.
Article in Journal of the Royal Statistical Society. Series B, Statistical methodology, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 70 papers.
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70 citing papers in PubMed.
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- PENALIZED REGRESSION FOR MULTIPLE TYPES OF MANY FEATURES WITH MISSING DATA.Statistica Sinica · 2023Article
- Identification of prognostic and predictive biomarkers in high-dimensional data with PPLasso.BMC bioinformatics · 2023Article
- Estimation of the number of spiked eigenvalues in a covariance matrix by bulk eigenvalue matching analysis.Journal of the American Statistical Association · 2023Article
- HIGH-DIMENSIONAL FACTOR REGRESSION FOR HETEROGENEOUS SUBPOPULATIONS.Statistica Sinica · 2023Article
- Cross-Validated Loss-Based Covariance Matrix Estimator Selection in High Dimensions.Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America · 2023Article
- Estimation of Large-Dimensional Covariance Matrices via Second-Order Stein-Type Regularization.Entropy (Basel, Switzerland) · 2022Article
- High-dimensional principal component analysis with heterogeneous missingness.Journal of the Royal Statistical Society. Series B, Statistical methodology · 2022Article
- Bayesian Factor-adjusted Sparse Regression.Journal of econometrics · 2022Article
10 more citing papers are in PubMed but not listed here.
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3 authors.
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Abstract
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 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 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 verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.
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