An Overview on the Estimation of Large Covariance and Precision Matrices
By Jianqing Fan, Yuan Liao. 2015
417 citations recorded by the source corpus.
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.
View Paper: https://www.semanticscholar.org/paper/cfc459e33b420e0ed4ee2092424f56735cc7f6d9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Bruce A. Craig
- Anindya Bhadra
- Clifford Lam
- Jianqing Fan
- Tommaso Cai
- Yuan Liao
- Lingzhou Xue
- Olivier Ledoit
Citations in the corpus
- A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices (2016, unknown): “Another example is from financial studies [20, 21, 22].”
- High‐dimensional covariance matrix estimation (2019, background): “See two nice reviews by Cai et al. (2016b) and Fan et al. (2016), with the former focused more on minimax adaptive estimations and related theoretical properties and bounds, while the latter focused on regularization methods leading to consistent estimation, including thresholding, penalized…”
- The Graphical Horseshoe Estimator for Inverse Covariance Matrices (2017, methodology): “so and SCAD are widely-used methods with good asymptotic properties, the element-wise bias of graphical lasso estimates can be large, and graphical SCAD does not guarantee positive definite estimates (Fan et al., 2016). To provide an alternative that remedies the accumulation of errors in high dimen5”
- Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Models (2020, unknown): “As for the covariance term c(v;θ), we estimate it with the sample covariance matrix [4], and the resulting variational estimate is”