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

Zhang Haixiang, Zheng Yinan, Zhang Zhou, Gao Tao, Joyce Brian, Zhang Wei, Hou Lifang, Liu Lei (), Yoon Grace, Schwartz Joel, Vokonas Pantel, Colicino Elena and Baccarelli Andrea
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Zhang Haixiang: Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China
Liu Lei: Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA
Yoon Grace: Department of Statistics, 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

Statistical Applications in Genetics and Molecular Biology, 2017, vol. 16, issue 3, 159-171

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).

Keywords: high-dimensional responses; multivariate regression; oracle inequality; tuning-insensitive; weighted square-root LASSO (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1515/sagmb-2016-0073

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