contamination ($\delta=0$). MCM(W) stands for the estimation performed by the Weiszfeld’s algorithm whereas MCM(R) denotes the averaged recursive approach and MCM(R+) its non negative modification (see equation \[def:gammamodif\]).[]{data-label="fig:boxerr0"}](MCMd50n200s500.pdf){height="10cm" width="15.5cm"}

![Estimation errors (at a logarithmic scale) over 500 Monte Carlo replications, for $n=200$, $d=50$ and a contamination by a $t$ distribution with 2 degrees of freedom with $\delta=0.02$. MCM(W) stands for the estimation performed by the Weiszfeld’s algorithm whereas MCM(R) denotes the averaged recursive approach and MCM(R+), its non negative modification with learning steps as in (\[def:gammamodif\]).[]{data-label="fig:boxerr"}](MCMd50n200s490.pdf){height="10cm" width="15.5cm"}

We first compare the performances of the two estimators of the MCM based on the Weiszfeld’s algorithm and the recursive algorithms (see (\[def:Gammamedaver\])) with more classical robust PCA techniques.

We generated samples of $Y$ with size $n=500$ and dimension $d \in \{50,200\}$, over 500 replications. Different levels of contamination are considered : $\delta \in \{0, 0.02, 0.05, 0.10, 0.20 \}$. For both dimensions $d =50$ and $d=200$, the first eigenvalue of the covariance matrix of $X$ represents about 81 % of the total variance, and the second one about 9 %.

  ------- -------- -------- -------- --------- -------- -------- --------
            PCA      MCD     MCM(W)   MCM(R+)   MCM(R)   SphPCA     PP
   d=50    0.0156   0.0199   0.0208   0.0211    0.0243   0.0287   