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.
@article{1176345705,
author = {Bednarski, Tadeusz},
title = {Binary Experiments, Minimax Tests and 2-Alternating Capacities},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 226-232},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345705}
}
Bednarski, Tadeusz. Binary Experiments, Minimax Tests and 2-Alternating Capacities. Ann. Statist., Tome 10 (1982) no. 1, pp. 226-232. http://gdmltest.u-ga.fr/item/1176345705/