content_image/294955.jpg
<img src='content_image/294955.jpg'>

follow essentially the same pattern. For m ≤ 4 . 8 (approximately) the τ - and MM- estimates have similar behaviors, both outperforming the S-estimate. For m > 4 . 8 the S- and MM-estimates have similar behaviors, both outperforming the τ -estimate. For q = 5 and x$_{0}$ = 10 (figure 4) the behavior of the robust estimates is similar to the one observed for q = 2 and x$_{0}$ = 10 (figure 2). 

## 9 An example with real data 

In this Section we analyze a dataset corresponding to electron-probe X ray micro- analysis of archeological glass vessels (Janssens et al., [12]). For each of n = 180 vessels we have a spectrum on 1920 frequencies and the contents of 13 chemical compounds; the purpose is to predict the contents on the basis of the spectra. In order to limit the size of our data set, we considered only two compounds (responses): P$_{2}$O$_{5}$ and PbO; and chose 12 equispaced frequencies between 100 to 400. This interval was chosen because the values of x$_{ij}$ are almost null for frequencies below 100 and above 400. We have therefore p = 13 and q = 2. 

We considered two multivariate regression estimates: the MLE and our MM- 

