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An overview of the estimation of large covariance and precision matrices

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  1. Shi Yafeng & Ai Chunrong & Yanlong Shi & Ying Tingting & Xu Qunfang, 2023. "Large covariance estimation using a factor model with common and group‐specific factors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(8), pages 2217-2248, December.
  2. Andrew Shephard & Xu Cheng & Alejándro Sanchez-Becerra, 2023. "How to weight in moments matchings: A new approach and applications to earnings dynamics," CeMMAP working papers 13/23, Institute for Fiscal Studies.
  3. Maurizio Daniele & Winfried Pohlmeier & Aygul Zagidullina, 2018. "Sparse Approximate Factor Estimation for High-Dimensional Covariance Matrices," Working Paper Series of the Department of Economics, University of Konstanz 2018-07, Department of Economics, University of Konstanz.
  4. Shaoxin Wang & Hu Yang & Chaoli Yao, 2019. "On the penalized maximum likelihood estimation of high-dimensional approximate factor model," Computational Statistics, Springer, vol. 34(2), pages 819-846, June.
  5. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Cross-validated covariance estimators for high-dimensional minimum-variance portfolios," Papers 1910.13960, arXiv.org, revised Oct 2020.
  6. Yunxi Zhang & Soeun Kim, 2024. "Gaussian Graphical Model Estimation and Selection for High-Dimensional Incomplete Data Using Multiple Imputation and Horseshoe Estimators," Mathematics, MDPI, vol. 12(12), pages 1-15, June.
  7. Wu, Zeyu & Wang, Cheng, 2022. "Limiting spectral distribution of large dimensional Spearman’s rank correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
  8. Benoît Carmichael & Gilles Boevi Koumou & Kevin Moran, 2023. "Unifying Portfolio Diversification Measures Using Rao’s Quadratic Entropy," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(4), pages 769-802, December.
  9. Minseog Oh & Donggyu Kim, 2024. "Property of Inverse Covariance Matrix-based Financial Adjacency Matrix for Detecting Local Groups," Papers 2412.05664, arXiv.org.
  10. Denis Belomestny & Mathias Trabs & Alexandre Tsybakov, 2017. "Sparse covariance matrix estimation in high-dimensional deconvolution," Working Papers 2017-25, Center for Research in Economics and Statistics.
  11. Anne Opschoor & André Lucas & István Barra & Dick van Dijk, 2021. "Closed-Form Multi-Factor Copula Models With Observation-Driven Dynamic Factor Loadings," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 1066-1079, October.
  12. Paolo Vidoni, 2021. "Boosting multiplicative model combination," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 761-789, September.
  13. Mei Choi Chiu & Chi Seng Pun & Hoi Ying Wong, 2017. "Big Data Challenges of High‐Dimensional Continuous‐Time Mean‐Variance Portfolio Selection and a Remedy," Risk Analysis, John Wiley & Sons, vol. 37(8), pages 1532-1549, August.
  14. Marilena Mitrouli & Athanasios Polychronou & Paraskevi Roupa & Ondřej Turek, 2021. "Estimating the Quadratic Form x T A −m x for Symmetric Matrices: Further Progress and Numerical Computations," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
  15. Vahe Avagyan, 2022. "Precision matrix estimation using penalized Generalized Sylvester matrix equation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 950-967, December.
  16. Enrico Bernardi & Matteo Farnè, 2022. "A Log-Det Heuristics for Covariance Matrix Estimation: The Analytic Setup," Stats, MDPI, vol. 5(3), pages 1-11, July.
  17. Hengxu Lin & Dong Zhou & Weiqing Liu & Jiang Bian, 2021. "Deep Risk Model: A Deep Learning Solution for Mining Latent Risk Factors to Improve Covariance Matrix Estimation," Papers 2107.05201, arXiv.org, revised Oct 2021.
  18. Xu, Hao & Gardoni, Paolo, 2020. "Conditional formulation for the calibration of multi-level random fields with incomplete data," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
  19. Lars Heinrich & Antoniya Shivarova & Martin Zurek, 2021. "Factor investing: alpha concentration versus diversification," Journal of Asset Management, Palgrave Macmillan, vol. 22(6), pages 464-487, October.
  20. Wei Dong & Hongzhen Liu, 2024. "Distributed Sparse Precision Matrix Estimation via Alternating Block-Based Gradient Descent," Mathematics, MDPI, vol. 12(5), pages 1-15, February.
  21. Ata Kabán & Efstratios Palias, 2024. "A Bhattacharyya-type Conditional Error Bound for Quadratic Discriminant Analysis," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-17, December.
  22. Aaron J Molstad & Adam J Rothman, 2018. "Shrinking characteristics of precision matrix estimators," Biometrika, Biometrika Trust, vol. 105(3), pages 563-574.
  23. Anders Bredahl Kock & David Preinerstorfer, 2024. "Enhanced power enhancements for testing many moment equalities: Beyond the $2$- and $\infty$-norm," Papers 2407.17888, arXiv.org, revised Oct 2024.
  24. Farnè, Matteo & Montanari, Angela, 2020. "A large covariance matrix estimator under intermediate spikiness regimes," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
  25. Morrison, Rebecca & Baptista, Ricardo & Basor, Estelle, 2022. "Diagonal nonlinear transformations preserve structure in covariance and precision matrices," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
  26. Mörstedt, Torsten & Lutz, Bernhard & Neumann, Dirk, 2024. "Cross validation based transfer learning for cross-sectional non-linear shrinkage: A data-driven approach in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 318(2), pages 670-685.
  27. Zou, Tao & Lan, Wei & Li, Runze & Tsai, Chih-Ling, 2022. "Inference on covariance-mean regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 318-338.
  28. Evan L. Reynolds & Brian C. Callaghan & Michael Gaies & Mousumi Banerjee, 2023. "Regression Trees and Ensemble for Multivariate Outcomes," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 77-109, May.
  29. Jianqing Fan & Donggyu Kim & Minseok Shin, 2024. "Adaptive Robust Large Volatility Matrix Estimation Based on High-Frequency Financial Data," Working Papers 202419, University of California at Riverside, Department of Economics.
  30. Kashlak, Adam B., 2021. "Non-asymptotic error controlled sparse high dimensional precision matrix estimation," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
  31. McGillivray, Annaliza & Khalili, Abbas & Stephens, David A., 2020. "Estimating sparse networks with hubs," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
  32. Yutong Lu & Gesine Reinert & Mihai Cucuringu, 2023. "Co-trading networks for modeling dynamic interdependency structures and estimating high-dimensional covariances in US equity markets," Papers 2302.09382, arXiv.org, revised May 2024.
  33. Huangdi Yi & Qingzhao Zhang & Cunjie Lin & Shuangge Ma, 2022. "Information‐incorporated Gaussian graphical model for gene expression data," Biometrics, The International Biometric Society, vol. 78(2), pages 512-523, June.
  34. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
  35. Zhou Tang & Zhangsheng Yu & Cheng Wang, 2020. "A fast iterative algorithm for high-dimensional differential network," Computational Statistics, Springer, vol. 35(1), pages 95-109, March.
  36. Ning Zhang & Jin Yang, 2023. "Sparse precision matrix estimation with missing observations," Computational Statistics, Springer, vol. 38(3), pages 1337-1355, September.
  37. Chen, Dachuan & Mykland, Per A. & Zhang, Lan, 2024. "Realized regression with asynchronous and noisy high frequency and high dimensional data," Journal of Econometrics, Elsevier, vol. 239(2).
  38. Donggyu Kim & Minseog Oh, 2024. "Property of Inverse Covariance Matrix-based Financial Adjacency Matrix for Detecting Local Groups," Working Papers 202420, University of California at Riverside, Department of Economics.
  39. Anna Bykhovskaya & Vadim Gorin, 2023. "High-Dimensional Canonical Correlation Analysis," Papers 2306.16393, arXiv.org, revised Jan 2025.
  40. Lim Hao Shen Keith, 2024. "Covariance Matrix Analysis for Optimal Portfolio Selection," Papers 2407.08748, arXiv.org.
  41. Shin, Minseok & Kim, Donggyu & Fan, Jianqing, 2023. "Adaptive robust large volatility matrix estimation based on high-frequency financial data," Journal of Econometrics, Elsevier, vol. 237(1).
  42. Khai X. Chiong & Hyungsik Roger Moon, 2017. "Estimation of Graphical Models using the $L_{1,2}$ Norm," Papers 1709.10038, arXiv.org, revised Oct 2017.
  43. Min Dai & Hanqing Jin & Steven Kou & Yuhong Xu, 2021. "A Dynamic Mean-Variance Analysis for Log Returns," Management Science, INFORMS, vol. 67(2), pages 1093-1108, February.
  44. David Neděla & Sergio Ortobelli Lozza & Tomáš Tichý, 2025. "Dynamic Return Scenario Generation Approach for Large-Scale Portfolio Optimisation Framework," Computational Economics, Springer;Society for Computational Economics, vol. 65(2), pages 819-843, February.
  45. Zhang, Qingzhao & Ma, Shuangge & Huang, Yuan, 2021. "Promote sign consistency in the joint estimation of precision matrices," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
  46. M. Perrot‐Dockès & C. Lévy‐Leduc & L. Rajjou, 2022. "Estimation of large block structured covariance matrices: Application to ‘multi‐omic’ approaches to study seed quality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 119-147, January.
  47. Florian Huber & Gary Koop & Massimiliano Marcellino & Tobias Scheckel, 2024. "Bayesian modelling of VAR precision matrices using stochastic block networks," Papers 2407.16349, arXiv.org.
  48. Krivobokova, Tatyana & Serra, Paulo & Rosales, Francisco & Klockmann, Karolina, 2022. "Joint non-parametric estimation of mean and auto-covariances for Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
  49. Gautam Sabnis & Debdeep Pati & Anirban Bhattacharya, 2019. "Compressed Covariance Estimation with Automated Dimension Learning," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 466-481, December.
  50. Linton, Oliver B. & Tang, Haihan, 2022. "Estimation Of The Kronecker Covariance Model By Quadratic Form," Econometric Theory, Cambridge University Press, vol. 38(5), pages 1014-1067, October.
  51. Lucija v{Z}igni'c & Stjepan Beguv{s}i'c & Zvonko Kostanjv{c}ar, 2024. "Block-diagonal idiosyncratic covariance estimation in high-dimensional factor models for financial time series," Papers 2407.03781, arXiv.org.
  52. Kim, Seungkyu & Park, Seongoh & Lim, Johan & Lee, Sang Han, 2023. "Robust tests for scatter separability beyond Gaussianity," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
  53. Yan Zhang & Jiyuan Tao & Zhixiang Yin & Guoqiang Wang, 2022. "Improved Large Covariance Matrix Estimation Based on Efficient Convex Combination and Its Application in Portfolio Optimization," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
  54. Zhentao Shi & Liangjun Su & Tian Xie, 2020. "L2-Relaxation: With Applications to Forecast Combination and Portfolio Analysis," Papers 2010.09477, arXiv.org, revised Aug 2022.
  55. Lidan Tan & Khai X. Chiong & Hyungsik Roger Moon, 2018. "Estimation of High-Dimensional Seemingly Unrelated Regression Models," Papers 1811.05567, arXiv.org.
  56. Fagbohungbe, Taiwo & Zhang, Liangliang & Cao, Xuan, 2025. "Sparse inverse covariance selection with mass-nonlocal priors," Statistics & Probability Letters, Elsevier, vol. 219(C).
  57. Wang, Shaoxin, 2021. "An efficient numerical method for condition number constrained covariance matrix approximation," Applied Mathematics and Computation, Elsevier, vol. 397(C).
  58. Kolli, Praveen & Sarantsev, Andrey, 2019. "Large rank-based models with common noise," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 29-35.
  59. Rasoul Lotfi & Davood Shahsavani & Mohammad Arashi, 2022. "Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method," Mathematics, MDPI, vol. 10(21), pages 1-13, November.
  60. Brownlees, Christian & Mesters, Geert, 2021. "Detecting granular time series in large panels," Journal of Econometrics, Elsevier, vol. 220(2), pages 544-561.
  61. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
  62. Monika Bours & Ansgar Steland, 2021. "Large‐sample approximations and change testing for high‐dimensional covariance matrices of multivariate linear time series and factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 610-654, June.
  63. Dong, Yingjie & Tse, Yiu-Kuen, 2020. "Forecasting large covariance matrix with high-frequency data using factor approach for the correlation matrix," Economics Letters, Elsevier, vol. 195(C).
  64. Zeyu Wu & Cheng Wang & Weidong Liu, 2023. "A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 619-648, August.
  65. Jonathan Tuck & Shane Barratt & Stephen Boyd, 2021. "Portfolio Construction Using Stratified Models," Papers 2101.04113, arXiv.org, revised Feb 2021.
  66. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2021. "Cross-validated covariance estimators for high-dimensional minimum-variance portfolios," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 35(3), pages 309-352, September.
  67. Peter C. B. Phillips & Liang Jiang, 2025. "Cross Section Curve Data Autoregression," Cowles Foundation Discussion Papers 2439, Cowles Foundation for Research in Economics, Yale University.
  68. De Nard, Gianluca & Zhao, Zhao, 2023. "Using, taming or avoiding the factor zoo? A double-shrinkage estimator for covariance matrices," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 23-35.
  69. Minshuo Chen & Renyuan Xu & Yumin Xu & Ruixun Zhang, 2025. "Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure," Papers 2504.06566, arXiv.org, revised May 2025.
  70. Wang, Hanchao & Peng, Bin & Li, Degui & Leng, Chenlei, 2021. "Nonparametric estimation of large covariance matrices with conditional sparsity," Journal of Econometrics, Elsevier, vol. 223(1), pages 53-72.
  71. Tomokaze Shiratori & Yuichi Takano, 2024. "DC algorithm for estimation of sparse Gaussian graphical models," PLOS ONE, Public Library of Science, vol. 19(12), pages 1-23, December.
  72. Evangelos E. Ioannidis, 2022. "A new non‐parametric cross‐spectrum estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 808-827, September.
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