ArticleAnnals of statistics2018
LARGE COVARIANCE ESTIMATION THROUGH ELLIPTICAL FACTOR MODELS.
Article in Annals of statistics, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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Who cites it
14 citing papers in PubMed.
- Deconfounded-Debiased Estimation and Inference for High-Dimensional Mediation Analysis With Pervasive Hidden Confounders.Statistics in medicine · 2026Article
- A Class of Structured High-Dimensional Dynamic Covariance Matrices.Communications in mathematics and statistics · 2025Article
- PENALIZED REGRESSION FOR MULTIPLE TYPES OF MANY FEATURES WITH MISSING DATA.Statistica Sinica · 2023Article
- Understanding Implicit Regularization in Over-Parameterized Single Index Model.Journal of the American Statistical Association · 2023Article
- Estimation of Large-Dimensional Covariance Matrices via Second-Order Stein-Type Regularization.Entropy (Basel, Switzerland) · 2022Article
- Simultaneous differential network analysis and classification for matrix-variate data with application to brain connectivity.Biostatistics (Oxford, England) · 2022Article
- Unified Principal Component Analysis for Sparse and Dense Functional Data under Spatial Dependency.Journal of business & economic statistics : a publication of the American Statistical Association · 2022Article
- A SHRINKAGE PRINCIPLE FOR HEAVY-TAILED DATA: HIGH-DIMENSIONAL ROBUST LOW-RANK MATRIX RECOVERY.Annals of statistics · 2021Article
- Robust high dimensional factor models with applications to statistical machine learning.Statistical science : a review journal of the Institute of Mathematical Statistics · 2021Article
- Integrating approximate single factor graphical models.Statistics in medicine · 2020Article
- Robust Covariance Estimation for Approximate Factor Models.Journal of econometrics · 2019Article
- LARGE COVARIANCE ESTIMATION THROUGH ELLIPTICAL FACTOR MODELS.Annals of statistics · 2018Article
- Article
- AnJournal of machine learning research : JMLR · 2018Article
Corrections and comments
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Authors and funding
3 authors.
Funding
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.
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Registered trials
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