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The spectral condition number plot for regularization parameter evaluation

Author

Listed:
  • Carel F. W. Peeters

    (Amsterdam University Medical Centers, Location VUmc)

  • Mark A. Wiel

    (Amsterdam University Medical Centers, Location VUmc
    University of Cambridge)

  • Wessel N. Wieringen

    (Amsterdam University Medical Centers, Location VUmc
    VU University Amsterdam)

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.

Suggested Citation

  • Carel F. W. Peeters & Mark A. Wiel & Wessel N. Wieringen, 2020. "The spectral condition number plot for regularization parameter evaluation," Computational Statistics, Springer, vol. 35(2), pages 629-646, June.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00912-z
    DOI: 10.1007/s00180-019-00912-z
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    References listed on IDEAS

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