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For the averaged recursive algorithms, we have considered tuning coefficients $c_m=c_\gamma = 2$ and a speed rate of $\alpha=3/4$. Note that the values of these tuning parameters have not been particularly optimised. We have noted that the simulation results were very stable, and did not depend much on the value of $c_m$ and $c_\gamma$ for $c_m, c_\gamma \in [1,20]$.

The estimation error of the eigenspaces associated to the largest eigenvalues is evaluated by considering the squared Frobenius norm between the associated orthogonal projectors. Denoting by $\mathbf{P}_q$ the orthogonal projector onto the space generated by the $q$ eigenvectors of the covariance matrix $\Sigma$ associated to the $q$ largest eigenvalues and by $\widehat{\mathbf{P}}_q$ an estimation, we consider the following loss criterion, $$\begin{aligned}
R(\widehat{\mathbf{P}}_q, \mathbf{P}_q) &= \mbox{tr} \left[ \left( \widehat{\mathbf{P}}_q - \mathbf{P}_q \right)^T \left( \widehat{\mathbf{P}}_q - \mathbf{P}_q \right) \right] \nonumber \\
 &= 2 q - 2 \mbox{tr} \left[ \widehat{\mathbf{P}}_q \mathbf{P}_q \right].
\label{def:errvecp} \end{aligned}$$ Note that we always have $R(\widehat{\mathbf{P}}_q, \mathbf{P}_q) \leq 2q$ and $R(\widehat{\mathbf{P}}_q, \mathbf{P}_q)=2q$ means that the eigenspaces generated by the true and the estimated eigenvectors are orthogonal.

Comparison with classical robust PCA techniques
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![Estimation errors (at a logarithmic scale) over 500 Monte Carlo replications, for $n=200$, $d=50$ with no 