Robust exponential squared loss-based estimation for partially linear additive panel data model with fixed effects

In this paper, we introduce a robust estimation method based on the exponential squared loss for partially linear additive panel data models with fixed effects. Our methodology involves eliminating fixed effects through auxiliary linear regression, approximating the nonparametric component using B-spline functions, and transforming the model into a parametric form. To obtain robust estimates of both parametric and nonparametric components, we optimize the corresponding loss function using exponential squared loss functions. Under certain regularity conditions, we establish the asymptotic properties of these estimators. Simulation studies are conducted to compare our methodology with the semiparametric least squares dummy variable estimator, demonstrating the superior robustness of our proposed approach. Additionally, we illustrate the practical utility of our method through an analysis of real data.