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Variable selection for covariate adjusted regression model

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Abstract

This paper employs the SCAD-penalized least squares method to simultaneously select variables and estimate the coefficients for high-dimensional covariate adjusted linear regression models. The distorted variables are assumed to be contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate. The authors show that under some appropriate conditions, the SCAD-penalized least squares estimator has the so called “oracle property”. In addition, the authors also suggest a BIC criterion to select the tuning parameter, and show that BIC criterion is able to identify the true model consistently for the covariate adjusted linear regression models. Simulation studies and a real data are used to illustrate the efficiency of the proposed estimation algorithm.

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China

    Xuejing Li, Jiang Du & Gaorong Li

  2. Department of Mathematics, Xuchang University, Xuchang, 461000, China

    Mingzhi Fan

Authors
  1. Xuejing Li
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  2. Jiang Du
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  3. Gaorong Li
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  4. Mingzhi Fan
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Corresponding author

Correspondence to Gaorong Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11471029, 11101014, 61273221 and 11171010, the Beijing Natural Science Foundation under Grant Nos. 1142002 and 1112001, the Science and Technology Project of Beijing Municipal Education Commission under Grant No. KM201410005010, the Research Fund for the Doctoral Program of Beijing University of Technology under Grant No. 006000543114550.

This paper was recommended for publication by Editor SUN Liuquan.

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Cite this article

Li, X., Du, J., Li, G. et al. Variable selection for covariate adjusted regression model. J Syst Sci Complex 27, 1227–1246 (2014). https://doi.org/10.1007/s11424-014-2276-9

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  • DOI: https://doi.org/10.1007/s11424-014-2276-9

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