Non parametric learning approach to estimate conditional quantiles in the dependent functional data case

In this paper, we focus on conditional quantile estimation when the covariates take their values in a bounded subspace of the functional space L2(T)${\bf L}^{2} (\cal {T})$, of square integrable random functions defined on some compact set T$\cal {T}$. We use a non parametric learning approach based on support vector machines (SVMs) technique. The main goal is to establish a weak consistency of the SVMs estimator of conditional quantile under exponentially strongly mixing functional input sequences. Our main result (the estimator satisfies an oracle inequality) extends a previous result for independent and identically distributed sample. We apply this estimator in practice through a real data set study.