Estimation in functional single-index varying coefficient model

Functional regression allows for a scalar response to be dependent on a functional predictor, however, not much work has been done when scalar predictors that interacts with the functional predictor are introduced. In this paper, we introduce a new functional single-index varying coefficient model with the functional predictor being single-index part. By means of functional principal components analysis and basis function approximation, we obtain the estimators of slope function and coefficient functions, and propose an iterative estimating procedure. Furthermore, the rates of convergence of the proposed estimators and the mean squared prediction error are established under some regularity conditions. At last, we illustrate the finite sample performance of our proposed methods with some simulation studies and a real data application.