Titre:  On the estimation of the density of a directional data
 
Resume: 
 
 Many directional data such as wind directions can be collected extremely easily so that experiments typically yield to a huge number of data points that are sequentially collected. To deal with such big data, the traditional nonparametric techniques rapidly require a lot of time to be computed and therefore become useless in practice if real time or online forecasts are expected. We propose a recursive version of the kernel density estimator for directional data  which (i) can be updated extremely easily when a new set of observations is available and (ii) keeps asymptotically the nice features of the same the usual  estimator.
Our methodology is based on Robbins-Monroe stochastic approximations ideas. We show that our estimator outperforms the traditional techniques in terms of computational time while being extremely competitive in terms of efficiency with respect to its competitors in the sequential context considered here. We obtain expressions for its asymptotic bias and variance together with an almost sure convergence rate and an asymptotic normality result. Our technique is illustrated on a wind dataset collected in Spain. A Monte-Carlo study confirms the nice properties of our recursive estimator with respect to its non-recursive counterpart.