content_image/309065.jpg content_image/309066.jpg content_image/309067.jpg content_image/309068.jpg
are taking B$_{0}$ = 0 , the estimate of the mean squared error (MSE) is given by 

<img src='content_image/309065.jpg'>

It must be recalled that the distributions of robust estimates under contami- nation are themselves heavy-tailed, and it is therefore prudent to evaluate their performance through robust measures (see [11] Sec. 1.4, p. 12, and [10] p.75). For this reason, we employed both MSE, and trimmed mean squared error (TMSE), which compute the 10% (upper) trimmed average of 

<img src='content_image/309066.jpg'>

The results given below correspond to this MSE, although the TMSE yields qual- itatively similar results (in the uncontaminated case the results are the same). 

## 8.2 Description of the estimators 

For each case, four estimates are computed: the MLE, an S-estimate, a τ -estimate and an MM-estimate. 

For the MLM, the S-estimates are defined by 

subject to 

where s is an M-estimate of scale. 

<img src='content_image/309067.jpg'>

<img src='content_image/309068.jpg'>

