is twofold. It provides efficient recursive estimation algorithms of the MCM that are able to deal with large samples of high dimensional data. By this recursive property, these algorithms can naturally deal with data that are observed sequentially and provide a natural update of the estimators at each new observation. Another advantage compared to classical approaches is that such recursive algorithms will not require to store all the data. Secondly, this work also aims at highlighting the interest of considering the median covariation matrix to perform principal components analysis of high dimensional contaminated data.

Different algorithms can be considered to get effective estimators of the MCM. When the dimension of the data is not too high and the sample size is not too large, Weiszfeld’s algorithm (see [@Weiszfeld1937] and [@VZ00]) can be directly used to estimate effectively both the geometric median and the median covariation matrix. When both the dimension and the sample size are large this static algorithm which requires to store all the data may be inappropriate and ineffective. We show how the algorithm developed by [@CCZ11] for the geometric median in Hilbert spaces can be adapted to estimate recursively and simultaneously the median as well as the 