VARIABLE SELECTION FOR COVARIATE ADJUSTED REGRESSION MODEL

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.