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March, 1982 Binary Experiments, Minimax Tests and 2-Alternating Capacities
Tadeusz Bednarski
Ann. Statist. 10(1): 226-232 (March, 1982). DOI: 10.1214/aos/1176345705


The concept of Choquet's 2-alternating capacity is explored from the viewpoint of Le Cam's experiment theory. It is shown that there always exists a least informative binary experiment for two sets of probability measures generated by 2-alternating capacities. This result easily implies the Neyman-Pearson lemma for capacities. Moreover, its proof gives a new method of construction of minimax tests for problems in which hypotheses are generated by 2-alternating capacities. It is also proved that the existence of least informative binary experiments is sufficient for a set of probability measures to be generated by a 2-alternating capacity. This gives a new characterization of 2-alternating capacities, closely related to that of Huber and Strassen.


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Tadeusz Bednarski. "Binary Experiments, Minimax Tests and 2-Alternating Capacities." Ann. Statist. 10 (1) 226 - 232, March, 1982.


Published: March, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0496.62004
MathSciNet: MR642734
Digital Object Identifier: 10.1214/aos/1176345705

Primary: 62G35
Secondary: 62B15

Keywords: binary experiments , Capacities , minimax testing , Robust testing

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 1 • March, 1982
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