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Regularized estimation in sparse high-dimensional multivariate regression, with application to a DNA methylation study

Author

Listed:
  • Zhang Haixiang

    (Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China)

  • Zheng Yinan

    (Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA)

  • Yoon Grace

    (Department of Statistics, Northwestern University, Chicago, IL 60611, USA)

  • Zhang Zhou

    (Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA)

  • Gao Tao

    (Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA)

  • Joyce Brian

    (Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA)

  • Zhang Wei

    (Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA)

  • Schwartz Joel

    (Department of Environmental Health, Harvard University, Boston, MA 02115, USA)

  • Vokonas Pantel

    (Department of Preventive Medicine, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA)

  • Colicino Elena

    (Normative Aging Study, Veterans Affairs Boston Healthcare System and Boston University, Boston, MA 02118, USA)

  • Baccarelli Andrea

    (Department of Environmental Health Sciences, Columbia University, New York, NY 10032, USA)

  • Hou Lifang

    (Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA)

  • Liu Lei

    (Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA)

Abstract

In this article, we consider variable selection for correlated high dimensional DNA methylation markers as multivariate outcomes. A novel weighted square-root LASSO procedure is proposed to estimate the regression coefficient matrix. A key feature of this method is tuning-insensitivity, which greatly simplifies the computation by obviating cross validation for penalty parameter selection. A precision matrix obtained via the constrained ℓ1 minimization method is used to account for the within-subject correlation among multivariate outcomes. Oracle inequalities of the regularized estimators are derived. The performance of our proposed method is illustrated via extensive simulation studies. We apply our method to study the relation between smoking and high dimensional DNA methylation markers in the Normative Aging Study (NAS).

Suggested Citation

  • Zhang Haixiang & Zheng Yinan & Yoon Grace & Zhang Zhou & Gao Tao & Joyce Brian & Zhang Wei & Schwartz Joel & Vokonas Pantel & Colicino Elena & Baccarelli Andrea & Hou Lifang & Liu Lei, 2017. "Regularized estimation in sparse high-dimensional multivariate regression, with application to a DNA methylation study," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(3), pages 159-171, August.
    • Handle: RePEc:bpj:sagmbi:v:16:y:2017:i:3:p:159-171:n:4
    DOI: 10.1515/sagmb-2016-0073
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    References listed on IDEAS

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