A robust partial linear model combining modified Huber loss function and variable selection

Partial linear models (PLMs), which contain both linear and nonlinear components, are flexible and more efficient than general nonparametric regression models. Typically, the estimation of PLMs is based on least squares or likelihood-based methods, which are very sensitive to outliers and may not be effective for heavy tail error distributions. This paper proposes a new, efficient, and robust estimation procedure based on a modified Huber loss function, in which the redundant covariates are also identified by a feature selection method simultaneously. Several simulation studies were conducted to assess the performance of the proposed model in the presence of outliers. Our simulation results demonstrate that the proposed model is efficient and robust against outliers and heavy-tailed distributions. Moreover, it demonstrates better performance in both prediction accuracy and variable selection compared to competing methods. Finally, the real Boston housing dataset is used to assess the proposed model.