Abstract
The least favorable pair (LFP) that Huber (1965), (1968) wrote down when he considered minimax test problems between neighborhoods of single probability measures $P_0, P_1$ defined in terms of $\varepsilon$-contamination and total variation is a canonical but only one possible choice of an LFP. We treat these neighborhoods by means of special capacities. The minimax test statistic is obtained by explicitly solving a minimization program, all LFP's are characterized by their $(P_0 + P_1)$-densities, another LFP is given explicitly. The technique is similar to that used by Huber and Strassen (1973), but is simpler and more constructive in this special situation.
Citation
Helmut Rieder. "Least Favorable Pairs for Special Capacities." Ann. Statist. 5 (5) 909 - 921, September, 1977. https://doi.org/10.1214/aos/1176343947
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