Non parametric estimation for data streams

We address news challenges related to non parametric estimation when the data are of complex nature (massive, sequentially observed according  time and space and infinite dimensional).  We focus on online estimation of the conditional variance Var(YIX = x), where the response Y is a real random variable and the covariate X takes values in an infinite-dimensional space. An estimator of the conditional variance is introduced when a sample  is supposed to be sequentially collected from a stationary and ergodic process satisfying a non-linear heteroscedastic functional regression model with martingale difference errors. Asymptotic results are established with convergence rates, whereas simulation studies show how the proposed estimator performs in terms of reducing the computational time without decreasing significantly the accuracy compared to its competitor. An application to real environmental data is also carried out to illustrate the online prediction of the volatility of maximum ozone concentration.