0$).

Furthermore it can be deduced easily that the MCM, which is a geometric median in the particular Hilbert spaces of Hilbert-Schmidt operators, is a robust indicator with a 50% breakdown point (see [@Kem87]) and a bounded sensitive gross error (see [@CCZ11]).

We also assume that

\[eq:invMomentCov\] There is a constant $C$ such that for all $h \in H$ and all $V \in \mathcal{S}(H)$ $$\begin{aligned}
 (a) &: \quad    {{\mathbb{E}}\left[ {\left\| (X- h)(X- h)^T - V \right\|}^{-1}_F \right]} \leq C. \\
 (b) &: \quad    {{\mathbb{E}}\left[ {\left\| (X- h)(X- h)^T - V \right\|}^{-2}_F \right]} \leq C. \\\end{aligned}$$

This assumption implicitly forces the distribution of $(X- h)(X- h)^T$ to have no atoms. It is more “likely” to be satisfied when the dimension $d$ of the data is large (see [@Cha92] and [@CCZ11] for a discussion). Note that it could be weakened as in [@CCZ11] by allowing points, necessarily different from the MCM $\Gamma_m$, to have strictly positive masses. Considering the particular case $V=0$, Assumption \[eq:invMomentCov\](a) implies that for all $h \in H$, $$\begin{aligned}
{{\mathbb{E}}\left[ \frac{1}{{\left\| X- h \right\|}^{2}} \right]} \leq C,
\label{cond:mominv2x}\end{aligned}$$ and this is not restrictive when the dimension $d$ of $H$ is equal or larger than 3.

Under Assumption \[eq:invMomentCov\](a), the 