Asymptotic properties of a nonparametric conditional distribution function estimator in the local linear estimation for functional data via a functional single-index model

This paper deals with the conditional distribution function estimator of a real response variable given a functional random variable (i.e takes values in an infinite dimensional space). Specifically, we focus on the functional index model, this approach represents a good compromise between nonparametric and parametric models. Then we give under general conditions and when the variables are independent, the quadratic error and asymptotic normality of estimator by local linear method, based on the single-index structure. Moreover, as an application, the asymptotic (1−γ) confidence interval of the conditional distribution function is given for 0 γ 1.