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• W2964287564 abstract "We propose a general Principal Orthogonal complEment Thresholding (POET) framework for large-scale covariance matrix estimation based on the approximate factor model. A set of high level sufficient conditions for the procedure to achieve optimal rates of convergence under different matrix norms is established to better understand how POET works. Such a framework allows us to recover existing results for sub-Gaussian data in a more transparent way that only depends on the concentration properties of the sample covariance matrix. As a new theoretical contribution, for the first time, such a framework allows us to exploit conditional sparsity covariance structure for the heavy-tailed data. In particular, for the elliptical distribution, we propose a robust estimator based on the marginal and spatial Kendall's tau to satisfy these conditions. In addition, we study conditional graphical model under the same framework. The technical tools developed in this paper are of general interest to high dimensional principal component analysis. Thorough numerical results are also provided to back up the developed theory." @default.
• W2964287564 created "2019-07-30" @default.
• W2964287564 creator A5019708503 @default.
• W2964287564 creator A5031910872 @default.
• W2964287564 creator A5080111161 @default.
• W2964287564 date "2018-08-01" @default.
• W2964287564 modified "2023-10-11" @default.
• W2964287564 title "Large covariance estimation through elliptical factor models" @default.
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• W2964287564 doi "https://doi.org/10.1214/17-aos1588" @default.
• W2964287564 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/6133289" @default.
• W2964287564 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/30214095" @default.
• W2964287564 hasPublicationYear "2018" @default.
• W2964287564 type Work @default.
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