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This contribution is part of the recent links between Functional Data and Big Data communities. A selected survey highlights how earlier ideas in high dimensional problems can be adapted in functional setting.

A fast and flexible k NN procedure is developed for dealing with a semiparametric functional regression model involving both partial-linear and single-index components. Rates of uniform consistency are presented. Simulated experiments highlight the advantages of the k NN procedure. A real data analysis is also shown.

This paper is on regression models when the explanatory variable is a function. The question is to look for which among the p n discretized values of the function must be incorporated in the model. The aim of the paper is to show how the continuous structure of the data allows to develop new specific variable selection procedures, which improve the rates of convergence of the estimated parameters and need much less restrictive assumptions on p n .

International audience; We study the nonparametric regression estimation when the explanatory variable takes values in some abstract functional space. We establish some asymptotic results and we give the (pointwise and uniform) convergence of the kernel type estimator constructed from functional data under long memory conditions.

We develop a nonparametric test, based on kernel smoothers, in order to decide whether some covariates could be suppressed in a multidimensional nonparametric regression study. We give the asymptotic distribution of the statistic involved in our test, under a general dependence assumption on the sample that allows for application to time series prediction.

Four nonparametric estimates of the mode of a density function are investigated. Two mode estimates are defined from a global (resp. from a local) kernel density estimate, while the other two are defined from a global (resp. from a local) kernel estimate of the first derivative of the density function. We show that each of these mode estimates attains the same rate of convergence as the usual sample model (Eddy, 1980). Then, Monte-Carlo simulations illustrate on finite samples the utility of the method based on the local estimate of the first derivative.

Data-driven smoothing selectors are defined for nonparametric hazard estimates. The selected parameters are shown to be asymptotically optimal with respect to integrated squared error.