Optimal robust estimates based on distances

Victor J. Yohai



Optimal robust M-estimates of a multidimensional parameter are described using Hampelís infïnitesimal approach. The optimal estimates are defined by minimizing a measure of efficiency under the model, subject to a bounded measure of infïnitesimal robustness. To this purpose we define measures of efficiency and infïnitesimal sensitivity based on the Kullback-Leibler divergence and on the Hellinger distance. We derive both optimal estimates and show that they coincide.