Empirical likelihood based modal regression

In this paper, we consider how to yield a robust empirical likelihood estimation for regression models. After introducing modal regression, we propose a novel empirical likelihood method based on modal regression estimation equations, which has the merits of both robustness and high inference efficiency compared with the least square based methods. Under some mild conditions, we show that Wilks’ theorem of the proposed empirical likelihood approach continues to hold. Advantages of empirical likelihood modal regression as a nonparametric approach are illustrated by constructing confidence intervals/regions. Two simulation studies and a real data analysis confirm our theoretical findings.