Robustness by generalized influence function : a new approach

The notion of influence function was introduced by Hampel and it plays a crucial role for the important applications in robustness analysis. It is defined by the derivative of a statistic at an underlying distribution and it describes the effect of an infinitesimal contamination at the point x on the estimate we are considering. We propose a new approach which can be used whenever the derivative doesn't exist. We extend the definition of influence function to nonsmooth functionals using a notion of generalized derivative. We also prove a generalized von Mises expansio