The scalar-on-function modal regression for functional time series data

Abstract

This paper develops a new nonparametric estimator of the scalar-on function modal regression that is used to analyse the co-variability between a functional regressor and a scalar output variable. The new estimator inherits the smoothness of the kernel method and the robustness of the quantile regression. We assume that the functional observations are structured as a strong mixing functional time series data and we establish the almost complete consistency (with rate) of the constructed estimator. A discussion highlighting the impact of this new estimator in nonparametric functional data analysis is also given. The usefulness of this new estimator is shown using an artificial data example.