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.
Acknowledgments
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which improved substantially the quality of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 We say that the sequence converges a.co. to zero, if and only if
Furthermore, we say that
, if there exists
such that