Robust estimation for partial functional linear additive model based on modal regression

Abstract

In this paper, we present a new robust estimation method based on modal regression for partial functional linear additive regression model, which combines the classic additive regression model with the functional linear regression model. Both the slope function and nonparametric additive functions are approximated by B-splines, and thus estimated through maximizing the modal objective function. Under some regularity conditions, we givethe convergence rates and asymptotic normality of the estimators. Finally, simulation studies and real data analysis are conducted to investigate the performance of the proposed methodologies, where it turns out that the estimators obtained are not only robust against outliers or heavy-tail error distributions, but also highly efficient as least squares estimators when the signal-noise ratio is high.