Current state of knowledge

We will work in an $\epsilon$-contamination neighborhood of a central distribution F₀. We will assume that the distribution F that generates the data satisfies

$$F \ \in \ {\cal Q}_\epsilon \left( F_0 \right) = \left\{ H... ... + \epsilon G, \ G \mbox{ an arbitrary distribution} \right\}$$ (1)

for a fixed $0 \le \epsilon < 1/2$. Roughly speaking, $\epsilon$ is the amount of contamination that affects our distribution of interest F₀. The theory of robust point estimation is fairly well developed. In what follows I am going to make a short review of some proposals for robust point estimates that have appeared in the literature. In the next section I will comment on the published results and reports on robust inference.