Summary
The change-of-variance curve (CVC) is generalized to M-estimators with piecewise continuous ψ-functions, in which case it becomes a Schwartz distribution. An M-estimator is called most B-robust when it minimizes Hampel's gross-error sensitivity γ *, and most V-robust when it minimizes the change-of-variance sensitivity k *. In the general case, the median is most B-robust and most V-robust. If consideration is restricted to redescending M-estimators, then the skipped median is most B-robust and the median-type tanh-estimator is most V-robust. By means of these results, complete solutions of the problems of optimal infinitesimal robustness are obtained.
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Rousseeuw, P.J. Most robust M-estimators in the infinitesimal sense. Z. Wahrscheinlichkeitstheorie verw Gebiete 61, 541–551 (1982). https://doi.org/10.1007/BF00531623
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DOI: https://doi.org/10.1007/BF00531623