Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

The main objective of this work is to estimate the conditional cumulative distribution using the nonparametric kernel method for a surrogated scalar response variable given a functional random one. We introduce the new kernel type estimator for the conditional cumulative distribution function (cond-cdf) of this kind of data. Afterwards, we estimate the quantiles by inverting this estimated cond-cdf and state the asymptotic properties. The pointwise almost complete convergence (with rate) of the kernel estimate of this model and the quantile estimator are established. Finally, a simulation study completed to show how our methodology can be adopted.

Keywords: functional data analysis (FDA); conditional distribution function; nonparametric kernel estimation; surrogate data; conditional quantile.