Robust estimation and variable selection in censored partially linear additive models

In this paper, we consider a new estimation in censored partially linear additive models in which the nonparametric components are approximated by polynomial spline. For identifying the significant variables in the linear part, a regularization procedure based on adaptive lasso is proposed for estimation and variable selection simultaneously. Under some regular conditions, the asymptotic normality and oracle property of the parametric components are established, and the convergence rates of the nonparametric components are obtained. Simulation studies and a real data analysis are presented to illustrate the behavior of the proposed estimators.