Estimation in nonparametric functional-on regression models with real responses

Abstract

In this article, we are interested in the estimation of the conditional distribution cumulative function and its regression by the kernel method for functional random variables. We present the theory, the practice and the applications of this nonparametric method, which uses a weighting function to smooth the data and obtain an estimation of the conditional distribution function. We illustrate the method with simulated example, and we discuss its limitations and future research perspectives. We show that the kernel method is simple, flexible and robust, and that it can handle complex cases of functional regression