Variable Selection and Estimation for Partially Linear Single-Index Errors-in-Variables Model

This paper focuses on variable selection and estimation for the partially linear single-index model, considering the presence of measurement errors in all variables. Based on local linear regression, SIMEX technique and profile least square method, we employ the smoothly clipped absolute deviation (SCAD) penalty method to simultaneously estimate parameters and select important variables. Under some regularity conditions, the asymptotic distributions and oracle property of the proposed estimators are obtained. Meanwhile, we discuss the implementation algorithm of the estimation and the selection of bandwidth and tuning parameters. Monte Carlo simulation studies are carried out to evaluate the finite sample behaviour of the proposed method. The results show that the variable selection and parameter estimation are effective.