Robust estimation for varying coefficient partially linear model based on MAVE

For the varying coefficient partially linear model, we propose a novel estimation method that combines robustness and efficiency by integrating the strengths of MAVE and local modal regression. The asymptotic properties of the proposed estimators indicate that this method not only addresses the issue of undersmoothing in nonparametric functions, but also remains robust and efficient in the presence of outliers and heavy-tailed error distributions. Moreover, only two bandwidth parameters are needed, and they are automatically selected through a data-driven procedure. Finally, simulation studies and real data examples are provided to evaluate the finite sample performance of the proposed method.