MCM(R+) its non negative modification whose learning weights are defined in (\[def:gammamodif\]).

If the size of the data $n \times d$ is not too large, an effective way for estimating $\Gamma_m$ is to employ Weiszfeld’s algorithm (see [@Weiszfeld1937] and [@VZ00] as well the Supplementary file for a description of the algorithms in our particular situation). The estimate obtained thanks to Weiszfeld’s algorithm is denoted by MCM(W) in the following. Note that other optimization algorithms which may be preferred in small dimension (see [@FFC2012]) have not been considered here since they would require the computation of the Hessian matrix, whose size is $d^4$, and this would lead to much slower algorithms. Note finally that all these alternative algorithms do not admit a natural updating scheme when the data arrive sequentially so that they should be completely ran again at each new observation.

Simulation protocol
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Independent realizations of a random variable $Y \in \mathbb{R}^d$ are drawn, where $$\begin{aligned}
Y &=& (1-O(\delta)) X + O(\delta) \epsilon,
\label{def:melange}\end{aligned}$$ is a mixture of two distributions and $X, O$ and $\epsilon$ are independent random variables. The random vector $X$ has a centered Gaussian distribution in $\mathbb{R}^d$ with covariance matrix $[\Sigma]_{\ell, j} = \min (\ell,j)/d$ and 