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Robust Variable Selection and Coefficient Estimation in Multivariate Multiple Regression Using LAD-Lasso

In: Modern Nonparametric, Robust and Multivariate Methods

Author

Listed:
  • Jyrki Möttönen

    (University of Helsinki, Department of Social Research)

  • Mikko J. Sillanpää

    (University of Oulu, Department of Mathematical Sciences and Biocenter Oulu)

Abstract

Univariate and multivariate lasso estimation methods are highly sensitive to outlying observations because of the sum of squared norms term in the objective function. Using sum of norms (least absolute deviations, LAD) instead of sum of squared norms gives us a considerably more robust estimate for the regression coefficients. In this paper we combine LAD with the multivariate lasso method and illustrate its estimation using simulated data set that are similar to those typically seen in association genetics. We will shortly consider also how the significance testing is done for non-zero coefficients and how the tuning parameter value can be determined.

Suggested Citation

  • Jyrki Möttönen & Mikko J. Sillanpää, 2015. "Robust Variable Selection and Coefficient Estimation in Multivariate Multiple Regression Using LAD-Lasso," Springer Books, in: Klaus Nordhausen & Sara Taskinen (ed.), Modern Nonparametric, Robust and Multivariate Methods, edition 1, chapter 0, pages 235-247, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22404-6_14
    DOI: 10.1007/978-3-319-22404-6_14
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