A Note on Huber's Robust Estimation of a Location Parameter

Huber, in his fundamental paper [1] and in [2], has considered the robust estimation of a location parameter and has obtained results which he applied to some examples including the ε-normal model, |ₓ|F(x) - Φ(x) ε, F symmetric\, when ε is sufficiently small (ε ε₀ ~ .03). In this note we show how his methods work for the family of distributions ∫A-A dF p, F symmetric\ and then use this to solve the ε-normal problem when ε > ε₀.