Open Access
2021 Estimating covariance and precision matrices along subspaces
Željko Kereta, Timo Klock
Electron. J. Statist. 15(1): 554-588 (2021). DOI: 10.1214/20-EJS1782


We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation accuracy depends almost exclusively on the components of the distribution that correspond to desired subspaces or directions. This is relevant and important for problems where the behavior of data along a lower-dimensional space is of specific interest, such as dimension reduction or structured regression problems. We also show that estimation of precision matrices is almost independent of the condition number of the covariance matrix. The presented applications include direction-sensitive eigenspace perturbation bounds, relative bounds for the smallest eigenvalue, and the estimation of the single-index model. For the latter, a new estimator, derived from the analysis, with strong theoretical guarantees and superior numerical performance is proposed.


Download Citation

Željko Kereta. Timo Klock. "Estimating covariance and precision matrices along subspaces." Electron. J. Statist. 15 (1) 554 - 588, 2021.


Received: 1 January 2020; Published: 2021
First available in Project Euclid: 12 January 2021

Digital Object Identifier: 10.1214/20-EJS1782

Primary: 62H12 , 62J10
Secondary: 62G05 , 62G08 , 62J12

Keywords: Covariance matrix , Dimension reduction , finite sample bounds , ordinary least squares , precision matrix , rate of convergence , Single-index model

Vol.15 • No. 1 • 2021
Back to Top