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...

The breakdown point in its different variants is one of the central notions to quantify the global robustness of a procedure. We propose a simple supplementary variant which is useful in situations where we have no obvious or only partial equivariance: Extending the Donoho and Huber (The notion...

Motivated by the information bound for the asymptotic variance of M-estimates for scale, we define Fisher information of scale of any distribution function F on the real line as the supremum of all , where [phi] ranges over the continuously differentiable functions with derivative of compact...