Robust estimation for partial functional linear regression models based on FPCA and weighted composite quantile regression

In this paper, we consider a novel estimation for partial functional linear regression models. The functional principal component analysis method is employed to estimate the slope function and the functional predictive variable, respectively. An efficient estimation based on principal component basis function approximation is used for minimizing the proposed weighted composite quantile regression (WCQR) objective function. Since the proposed WCQR involves a vector of weights, we develop a computational strategy for data-driven selection of the optimal weights. Under some mild conditions, the theoretical properties of the proposed WCQR method are obtained. The simulation study and a real data analysis are provided to illustrate the numerical performance of the resulting estimators.