A robust penalized estimation for identification in semiparametric additive models

Based on the modal regression estimation (Yao et al., 2012) and spline based estimation method, we provide a novel and robust approach to identify nonzero components as well as linear components in semiparametric additive models by applying a two-fold smoothly clipped absolute deviation (Fan and Li, 2001) penalty. The performance of the new method is demonstrated in terms of theoretical and simulation results.