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

Abstract

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 $\varepsilon$-normal model, $\{F|\sup_x|F(x) - \Phi(x)\mid \leqq \varepsilon, F \text{symmetric}\}$, when $\varepsilon$ is sufficiently small $(\varepsilon \leqq \varepsilon_0 \sim .03)$. In this note we show how his methods work for the family of distributions $\{F \mid \int^A_{-A} dF \geqq p, F \text{symmetric}\}$ and then use this to solve the $\varepsilon$-normal problem when $\varepsilon > \varepsilon_0$.