Graph-Guided Banding of the Covariance Matrix

Jacob Bien

Journal of the American Statistical Association, 2019, vol. 114, issue 526, 782-792

Abstract: Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse covariance) matrix is sparse, while making no particular structural assumptions on the desired pattern of sparsity. A highly-related, yet complementary, literature studies the specific setting in which the measured variables have a known ordering, in which case a banded population matrix is often assumed. While the banded approach is conceptually and computationally easier than asking for “patternless sparsity,” it is only applicable in very specific situations (such as when data are measured over time or one-dimensional space). This work proposes a generalization of the notion of bandedness that greatly expands the range of problems in which banded estimators apply. We develop convex regularizers occupying the broad middle ground between the former approach of “patternless sparsity” and the latter reliance on having a known ordering. Our framework defines bandedness with respect to a known graph on the measured variables. Such a graph is available in diverse situations, and we provide a theoretical, computational, and applied treatment of two new estimators. An R package, called ggb, implements these new methods. Supplementary materials for this article are available online.

Date: 2019
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2018.1442720 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:114:y:2019:i:526:p:782-792

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2018.1442720

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().