Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Matrix Nearness Problems with Bregman Divergences
SIAM Journal on Matrix Analysis and Applications
Computing a Nearest Correlation Matrix with Factor Structure
SIAM Journal on Matrix Analysis and Applications
IEEE Transactions on Signal Processing
Monitoring the covariance matrix with fewer observations than variables
Computational Statistics & Data Analysis
Robust methods for inferring sparse network structures
Computational Statistics & Data Analysis
| Hi-index | 0.03 |
The need to estimate structured covariance matrices arises in a variety of applications and the problem is widely studied in statistics. A new method is proposed for regularizing the covariance structure of a given covariance matrix whose underlying structure has been blurred by random noise, particularly when the dimension of the covariance matrix is high. The regularization is made by choosing an optimal structure from an available class of covariance structures in terms of minimizing the discrepancy, defined via the entropy loss function, between the given matrix and the class. A range of potential candidate structures comprising tridiagonal Toeplitz, compound symmetry, AR(1), and banded Toeplitz is considered. It is shown that for the first three structures local or global minimizers of the discrepancy can be computed by one-dimensional optimization, while for the fourth structure Newton's method enables efficient computation of the global minimizer. Simulation studies are conducted, showing that the proposed new approach provides a reliable way to regularize covariance structures. The approach is also applied to real data analysis, demonstrating the usefulness of the proposed approach in practice.