Robust estimation for dynamic single index varying coefficient models

In this article, we propose a new estimation procedure based on modal regression for dynamic single index varying coefficient models, where the index coefficient functions and the link functions are approximated by B-spline basis, respectively. Under some mild regularity conditions, we establish the asymptotic normalities of the obtained spline-based estimators. By introducing an additional tuning parameter (e.g. h), the proposed method can produce robust estimates when the data are not well behaved (e.g. in the presence of outliers and/or heavy-tailed error distributions), and we further calculate the robust estimates by using a modified expectation-maximization-type iteration algorithm, and develop a data driven procedure to select the tuning parameters for the proposed approaches. Finally, some simulations and a real data application are conducted to illustrate the utility of the proposed methodology.