  In the context of large samples, a small number of individuals might spoil
basic statistical indicators like the mean. It is difficult to detect
automatically these atypical individuals, and an alternative strategy is using
robust approaches. This paper focuses on estimating the geometric median of a
random variable, which is a robust indicator of central tendency. In order to
deal with large samples of data arriving sequentially, online stochastic Newton
algorithms for estimating the geometric median are introduced and we give their
rates of convergence. Since estimates of the median and those of the Hessian
matrix can be recursively updated, we also determine confidences intervals of
the median in any designated direction and perform online statistical tests.
