University of Oulu

M. O. Kuismin, J. T. Kemppainen & M. J. Sillanpää. Precision Matrix Estimation With ROPE. Journal of Computational and Graphical Statistics Vol. 26, Iss. 3,2017

Precision matrix estimation with ROPE

Saved in:
Author: Kuismin, M.O.1; Kemppainen, J. T.1; Sillanpää, M. J.2
Organizations: 1Department of Mathematical Sciences, University of Oulu, Oulu, Finland
2Department of Mathematical Sciences, Biocenter Oulu, University of Oulu, Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
Persistent link:
Language: English
Published: Informa, 2017
Publish Date: 2017-09-20


It is known that the accuracy of the maximum likelihood-based covariance and precision matrix estimates can be improved by penalized log-likelihood estimation. In this article, we propose a ridge-type operator for the precision matrix estimation, ROPE for short, to maximize a penalized likelihood function where the Frobenius norm is used as the penalty function. We show that there is an explicit closed form representation of a shrinkage estimator for the precision matrix when using a penalized log-likelihood, which is analogous to ridge regression in a regression context. The performance of the proposed method is illustrated by a simulation study and real data applications. Computer code used in the example analyses as well as other supplementary materials for this article are available online.

see all

Series: Journal of computational and graphical statistics
ISSN: 1061-8600
ISSN-E: 1537-2715
ISSN-L: 1061-8600
Volume: 26
Issue: 3
Pages: 682 - 694
DOI: 10.1080/10618600.2016.1278002
Type of Publication: A1 Journal article – refereed
Field of Science: 112 Statistics and probability
111 Mathematics
Funding: This work was supported by the University of Oulu’s Exactus Doctoral Programme.
Copyright information: ©2017 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 8 Jan 2017, available online: