We derive conditions for L2 differentiability of generalized linear models with error distributions not necessarily belonging to exponential families, covering both cases of stochastic and deterministic regressors. These conditions induce smoothness and integrability conditions for corresponding...

Abstract Generalizing MSE-optimality on 1/√ n -shrinking neighborhoods of contamination type, we determine the robust influence curve that minimizes maximum asymptotic risk, where risk may be any convex and isotone function G of L 2 - and L ∞ -norms. The solutions necessarily minimize the...

We determine the increase of the maximum risk over the minimax risk in the case that the optimally robust estimator for the false radius is used. This is done by numerical solution of the implicit equations which determine optimal robustness, for location, scale, and linear regression models,...