Variable selection for additive partially linear models with measurement error

Variable selection for additive partially linear models with measurement error is considered. By the backfitting technique, we first propose a variable selection procedure for the parametric components based on the smoothly clipped absolute deviation (SCAD) penalization, and one-step spare estimates for parametric components are also presented. The resulting estimates perform asymptotic normality as well as an oracle property. Then, two-stage backfitting estimators are also presented for the nonparametric components by using the local linear method, and the structures of asymptotic biases and covariances of the proposed estimators are the same as those in partially linear model with measurement error. The finite sample performance of the proposed procedures is illustrated by simulation studies.