The spectral condition number plot for regularization parameter evaluation

Carel F. W. Peeters (), Mark A. Wiel and Wessel N. Wieringen
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Carel F. W. Peeters: Amsterdam University Medical Centers, Location VUmc
Mark A. Wiel: Amsterdam University Medical Centers, Location VUmc
Wessel N. Wieringen: Amsterdam University Medical Centers, Location VUmc

Computational Statistics, 2020, vol. 35, issue 2, No 10, 629-646

Abstract: 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 assessment. The proposed tool is computationally friendly and can be employed for the full class of ridge-type covariance (precision) estimators.

Keywords: Eigenvalues; High-dimensional covariance (precision) estimation; $$\ell _2$$ ℓ 2 -Penalization; Matrix condition number (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00180-019-00912-z

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