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The Spectral Condition Number Plot for Regularization Parameter Determination

Authors :
Peeters, Carel F. W.
van de Wiel, Mark A.
van Wieringen, Wessel N.
Source :
Computational Statistics, 35(2):629-646, 2020
Publication Year :
2016

Abstract

Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample covariance matrix. These estimators depend on a penalty parameter and choosing its value can be hard, in terms of being computationally unfeasible or tenable only for a restricted set of ridge-type estimators. Here we introduce a simple graphical tool, the spectral condition number plot, for informed heuristic penalty parameter selection. The proposed tool is computationally friendly and can be employed for the full class of ridge-type covariance (precision) estimators.<br />Comment: 41 pages, 7 figures, includes supplementary material

Details

Database :
arXiv
Journal :
Computational Statistics, 35(2):629-646, 2020
Publication Type :
Report
Accession number :
edsarx.1608.04123
Document Type :
Working Paper
Full Text :
https://doi.org/10.1007/s00180-019-00912-z