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September, 1977 Least Favorable Pairs for Special Capacities
Helmut Rieder
Ann. Statist. 5(5): 909-921 (September, 1977). DOI: 10.1214/aos/1176343947


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.


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Helmut Rieder. "Least Favorable Pairs for Special Capacities." Ann. Statist. 5 (5) 909 - 921, September, 1977.


Published: September, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0371.62074
MathSciNet: MR468005
Digital Object Identifier: 10.1214/aos/1176343947

Primary: 62G35
Secondary: 62G35

Keywords: $\epsilon$-contamination , capacity , Least favorable pairs , minimax test problems , Total variation

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 5 • September, 1977
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