Global robustness of location and dispersion estimates

We analyze the global robustness of location and dispersion estimates using the concept of relative explosion rate. The merits of several dispersion estimates are compared when the dispersion parameter itself is of main interest and also when they are auxiliary estimates needed to define scale equivariant location M-estimates. We have also compared location M-estimates and found that the choice of score function (its shape) is of secondary importance in comparison with the choice of the tuning constant and the auxiliary dispersion estimate. Finally, we use the explosion rate to assess the combined effect of the tuning constant and auxiliary dispersion estimate on the global robustness properties of location M-estimates.