Spatial modelization: Local linear estimation of the conditional distribution for functional data

The main purpose of this paper is to estimate nonparametrically some characteristics of spatial models related to the conditional cumulative distribution of a scalar response given functional random variables by the local linear approach. Specifically, the local linear estimators of the conditional cumulative distribution function and of the successive derivatives of the conditional density are constructed. Then, the asymptotic properties of these estimators, in terms of the almost-complete convergence with rates, are stated. Moreover, the usefulness of our results is illustrated through their application (a) to the spatial conditional mode estimation and (b) to the soil chemistry properties data.