determinant one, i.e., for any positive definite matrix V with | V | = 1 Then, since | ˜ Γ ( k $^{+1)}$| = | ˜ Γ ( k $^{)}$| = 1, we have that (A.60) is ≤ 0. ■ Acknowledgements: We would like to thank the referees and the editor for their helpful comments and suggestions. This research was partially supported by grants PIP 216 from CONICET and PICT 899 from ANPCyT, Argentina. References n ∑ i =1 ω$_{i}$d 2 $_{i}$( ˜ B ( k $^{+1)}$, ˜ Γ ( k $^{)}$) ≤ n ∑ i =1 ω$_{i}$d 2 $_{i}$( ˜ B ( k $^{+1)}$, V ) . [1] Agull´ o J., Croux C., Van Aelst S. (2008). The Multivariate Least Trimmed Squares Estimator. Journal of Multivariate Analysis, 99, pp. 311 – 338. [2] Bai Z., Chen X., Wu Y. (2008). On constrained M-estimation and its recur- sive analog in multivariate linear regression models. Statistica Sinica, 18, pp. 405–424. [3] Berrendero J., Mendes B., Tyler D. (2007). On the maximum bias functions of MM-estimates and constrained M-estimates of regression. The Annals of Statistics, 35, pp. 13 – 40. [4] Bhatia R. (1952). Matrix Analysis. Springer. [5] Bilodeau M., Duchesne P. (2000). Robust estimation of the SUR model. Canad. J. Statist., 28, pp. 227–288. [6] Croux C., Rousseeuw P., H¨ ossjer O. (1994). Generalized S-estimators. Jour- nal of the American Statistical Association 89, pp. 1271-1281. 60