Precision matrix estimation with ROPE
Kuismin, M.O.; Kemppainen, J. T.; Sillanpää, M. J. (2017-01-08)
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
©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: http://www.tandfonline.com/10.1080/10618600.2016.1278002
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.
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