Summary
Solutions to minimax test problems between neighbourhoods generated by specially defined capacities are discussed. The capacities are superpositions of probability measures and concave functions, so the paper covers most of the earlier results of Huber and Rieder concerning minimax testing between ɛ-contamination and total variation neighbourhoods. It is shown that the Neyman-Pearson lemma for 2-alternating capacities, proved by Huber and Strassen, can be applied to test problems between noncompact neighbourhoods of probability measures. It turns out that the Radon-Nikodym derivative between the special capacities is usually a nondecreasing function of the truncated likelihood ratio of some probability measures.
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Bednarski, T. On solutions of minimax test problems for special capacities. Z. Wahrscheinlichkeitstheorie verw Gebiete 58, 397–405 (1981). https://doi.org/10.1007/BF00542644
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DOI: https://doi.org/10.1007/BF00542644