Abstract
We propose a new neighborhood of distributions for robust inference, which is generated by a certain special capacity with three constants. It covers not only the familiar neighborhoods defined in terms of ε-contamination, total variation and their combination, but also their intersections. It is shown that the neighborhood is also obtained from contaminating some neighborhood which consists of absolutely continuous distributions. We derive the explicit forms of Radon-Nikodym derivatives and the least favorable pairs for such special capacities and neighborhoods on the real line, which generalize the earlier results of Huber and Rieder for minimax testing, and reinforce the general results of Bednarski.
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