Non-parametric estimation of the conditional distribution function using the kernel method

Abstract

In this work, we were interested in the non-parametric estimation of the conditional distribution function, when the explanatory variable is functional and the response is real, by the kernel method. The main results we obtained are the following : First, we built a local constant of our estimator, then we established its uniform complete convergence by specifying its rate of convergence, when the observations are independent identically distributed. We also established the asymptotic normality of the same estimator by giving an explicit expression of the terms of bias and its the variance.