TY - JOUR
T1 - The Generalized Ridge Estimator of the Inverse Covariance Matrix
AU - van Wieringen, Wessel N.
N1 - Publisher Copyright: © 2019, © 2019 The Author(s). Published with License by Taylor & Francis Group, LLC. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/10/2
Y1 - 2019/10/2
N2 - The ridge inverse covariance estimator is generalized to allow for entry-wise penalization. An efficient algorithm for its evaluation is proposed. Its computational accuracy is benchmarked against implementations of specific cases the generalized ridge inverse covariance estimator encompasses. The proposed estimator shrinks toward a user-specified, nonrandom target matrix and is shown to be positive definite and consistent. It is pointed out how the generalized ridge inverse covariance estimator can be used to obtain a generalization of the graphical lasso estimator as well as of its elastic net counterpart. The usage of the presented estimator is illustrated in graphical modeling of omics data. Supplementary materials for this article are available online.
AB - The ridge inverse covariance estimator is generalized to allow for entry-wise penalization. An efficient algorithm for its evaluation is proposed. Its computational accuracy is benchmarked against implementations of specific cases the generalized ridge inverse covariance estimator encompasses. The proposed estimator shrinks toward a user-specified, nonrandom target matrix and is shown to be positive definite and consistent. It is pointed out how the generalized ridge inverse covariance estimator can be used to obtain a generalization of the graphical lasso estimator as well as of its elastic net counterpart. The usage of the presented estimator is illustrated in graphical modeling of omics data. Supplementary materials for this article are available online.
KW - Graphical lasso
KW - Multivariate normality
KW - Nonzero centered penalty
KW - Penalized estimation
KW - Precision matrix
UR - http://www.scopus.com/inward/record.url?scp=85067572862&partnerID=8YFLogxK
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U2 - https://doi.org/10.1080/10618600.2019.1604374
DO - https://doi.org/10.1080/10618600.2019.1604374
M3 - Article
SN - 1061-8600
VL - 28
SP - 932
EP - 942
JO - Journal of Computational and Graphical Statistics
JF - Journal of Computational and Graphical Statistics
IS - 4
ER -