Density estimation over spatio-temporal data streams

In the last few years, data can be collected extremely easily in many scientific research fields. This became possible by the recent technological advances that have made online monitoring possible. In such situations, if real time or online estimations are expected, the usual nonparametric techniques rapidly require a lot of time to be computed and therefore become useless in practice. Adaptative counterparts of the classical kernel density estimators, that can be updated extremely easily when a new set of observations is available are investigated, for spatio-temporal processes with weak dependence structures. Mean square, uniform almost sure convergences and a central limit result are obtained under general and easily verifiable conditions. The efficiency of the considered estimators is evaluated through simulations and a real data application. The results show that the proposed method works well within the framework of a spatio-temporal data stream.