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March, 1973 Minimax Tests and the Neyman-Pearson Lemma for Capacities
Peter J. Huber, Volker Strassen
Ann. Statist. 1(2): 251-263 (March, 1973). DOI: 10.1214/aos/1176342363

Abstract

Robust test problems between two approximately known simple hypotheses can be formalized as minimax test problems between two composite hypotheses. We show that if the composite hypotheses can be described in terms of alternating capacities of order 2 (in the sense of Choquet), then the minimax tests are ordinary Neyman-Pearson tests between a fixed representative pair of simple hypotheses; moreover, the condition is in a certain sense also necessary. All the neighborhoods customarily used to formalized approximate knowledge happen to have this particular structure.

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Peter J. Huber. Volker Strassen. "Minimax Tests and the Neyman-Pearson Lemma for Capacities." Ann. Statist. 1 (2) 251 - 263, March, 1973. https://doi.org/10.1214/aos/1176342363

Information

Published: March, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0259.62008
MathSciNet: MR356306
Digital Object Identifier: 10.1214/aos/1176342363

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 2 • March, 1973
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