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Abstract
As the problem of prediction is of great interest, several tools based on different methods and devoted to various contexts, have been developed in the statistical literature. The contribution of this paper is to focus on the study of the local linear nonparametric estimation of the quantile of a scalar response variable given a functional covariate. In fact, the covariate is a random variable taking values in a semi-metric space which can have an infinite dimension in order to permit to deal with curves. We first establish pointwise and uniform almost-complete convergences, with rates, of the conditional distribution function estimator. Then, we deduce the uniform almost-complete convergence of the obtained local linear conditional quantile estimator. We also bring out the application of our results to the multivariate case as well as to the particular case of the kernel method. Moreover, a real data study allows to place our conditional median estimator in relation to several other predictive tools.