Robust exponential squared loss-based estimation in semi-functional linear regression models

In this paper, we present a new robust estimation procedure for semi-functional linear regression models by using exponential squared loss. The outstanding advantage of the proposed method is the resulting estimators are more efficient than the least squares estimators in the presence of outliers or heavy-tail error distributions. The slope function and functional predictor variable are approximated by functional principal component basis functions. Under some regularity conditions, we obtain the optimal convergence rate of slope function, and the asymptotic normality of parameter vector and variance estimator. Finally, we investigate the finite sample performance of the proposed method through a simulation study and real data analysis.