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The high dimensional setting is a modern and dynamic research area in Statistics. It covers numerous situations where the number of explanatory variables is much larger than the sample size. Last fifteen years have been devoted to develop new methodologies able to manage high dimensional data including the so-called functional data (which can be viewed as a special case of high dimensional data with a high correlated structure). Statistical modelling involving only linear relationship have been essentially studied. However, it is well known in the nonparametrician communauty that taking into account nonlinearities may improve significantly the predictive power of the statistical methods and also may reveal relevant informations allowing to better understand the observed phenomenon. This talk presents recent advances with respect to both issues : functional nonparametric approach to estimate nonlinear relationship involving functional data (through functional kernel regression estimator) and multivariate approach to propose nonlinear variable selection method in high dimensional setting. Some simulations and real datasets will illustrate our purpose.
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