Within the framework of big-data, we are very often led to treat a voluminous set of data.
First, we consider stochastic algorithms to build recursive estimators. The major interest of these recursive approaches is that they allow a quick update of the data.
We then focus on the problem of recursive estimation of a regression function in the case of functional data, we present some results concerning the asymptotic behavior of the proposed non-parametric estimator, we then proposed a data-driven bandwidth selection procedure of the smoothing parameter and we compare the proposed method with existing methods using simulated data and then real data.
Moreover, we address the problem of the supervised classification of curves, we underline the gain of the use of recursive approaches using data simulated and then real data.
Finally, we consider the problem of the unsupervised classification using an application example from the field of Psychology more precisely in electroencephalography (EEG) which underlines the practical interest of the method and we compare our approach to a parametric approach based on the Stochastic Block Model (SBM).
