mlsanityData to 14 Oct 2026

An Overview on the Estimation of Large Covariance and Precision Matrices

arXiv 1504.02995 ↗First posted 12 Apr 2015stat.MEcited by 21

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Abstract (arXiv)

Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations between variables, while the precision matrix encodes conditional correlations between pairs of variables given the remaining variables. In this paper, we provide a selective review of several recent developments on estimating large covariance and precision matrices. We focus on two general approaches: rank based method and factor model based method. Theories and applications of both approaches are presented. These methods are expected to be widely applicable to analysis of economic and financial data.

Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Apr 2015.

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Citing papers per year: 2021: 4; 2022: 4; 2023: 1; 2024: 5; 2025: 2; 2026: 5.

21 papers.

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  1. 2021Affine-Invariant Integrated Rank-Weighted Depth: Definition, Properties and Finite Sample Analysiscited by 8
  2. 2024Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrixcited by 8
  3. 2023Quantum State Tomography using Quantum Machine Learningcited by 7
  4. 2021Deep Risk Model: A Deep Learning Solution for Mining Latent Risk Factors to Improve Covariance Matrix Estimationcited by 5
  5. 2021Diagonal Nonlinear Transformations Preserve Structure in Covariance and Precision Matricescited by 4
  6. 2025Diffusion differentiable resamplingcited by 2
  7. 2024Double Descent: Understanding Linear Model Estimation of Nonidentifiable Parameters and a Model for Overfittingcited by 1
  8. 2026A General ReLearner: Empowering Spatiotemporal Prediction by Re-learning Input-label Residualcited by 1
  9. 2026Identification and Inference in Nonlinear Dynamic Network Modelscited by 1
  10. 2021Robust Classification via Support Vector Machinescited by 0
  11. 2022Recover the spectrum of covariance matrix: a non-asymptotic iterative methodcited by 0
  12. 2022Inference of Multiscale Gaussian Graphical Modelcited by 0
9 more
  1. 2022State space partitioning based on constrained spectral clustering for block particle filteringcited by 0
  2. 2022Pitfalls of Climate Network Construction: A Statistical Perspectivecited by 0
  3. 2024DC Algorithm for Estimation of Sparse Gaussian Graphical Modelscited by 0
  4. 2024Distributed Networked Multi-task Learningcited by 0
  5. 2024Asymptotic spectrum of weighted sample covariance: another proof of spectrum convergencecited by 0
  6. 2025Block Toeplitz Sparse Precision Matrix Estimation for Large-Scale Interval-Valued Time Series Forecastingcited by 0
  7. 2026A Resampling-Based Framework for Network Structure Learning in High-Dimensional Datacited by 0
  8. 2026Enhancing a Risk Model by Adding Transient Statistical Factorscited by 0
  9. 2026Selective Inference for Clustering Under Unknown Covariancecited by 0