Robust estimation for partially linear additive panel data models with fixed effects based on auxiliary regression

This paper presents a robust estimation method for partially linear additive panel data models with fixed effects. To eliminate the impact of fixed effects on both parametric and nonparametric estimators, we employ an auxiliary linear regression for fixed-effect adjustment and utilise B-spline functions to approximate the nonparametric components of the model. By constructing a composite quantile regression objective function, we simultaneously obtain estimators for both the parametric and nonparametric components. Under certain regularity conditions, we demonstrate the asymptotic properties of the proposed estimators. The MM algorithm is implemented to determine the optimal solution for the objective function. To evaluate the effectiveness of our method, we conduct simulation studies and compare our proposed method with the least squares dummy variable method and the two-stage local polynomial estimator. The results indicate that our proposed method performs better and is more robust when the model errors are non-normally distributed.