Statistical inference in the partial linear models with the double smoothing local linear regression method

Statistical inference about a partial linear model includes two parts, one linear and the other nonparametric. The double smoothing method proposed by He and Huang (2009) is a progressive local smoothing method for nonparametric curve estimation. In this paper, we discuss its extension to partial linear models, accompanied with difference-based estimation method for the linear part. Asymptotic theory of the proposed method is developed. The results of simulation studies and real data examples demonstrate that our approach is effective even for data with moderate sample sizes.