On combinatorial testing problems
Louigi Addario-Berry, Nicolas Broutin, Luc Devroye, and Gábor Lugosi
Source: Ann. Statist. Volume 38, Number 5
(2010), 3063-3092.
Abstract
We study a class of hypothesis testing problems in which, upon observing the realization of an n-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether there is a subset of the components belonging to a certain given class of sets whose elements have been “contaminated,” that is, have a mean different from zero. We establish some general conditions under which testing is possible and others under which testing is hopeless with a small risk. The combinatorial and geometric structure of the class of sets is shown to play a crucial role. The bounds are illustrated on various examples.
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1283175989
Digital Object Identifier: doi:10.1214/10-AOS817
Zentralblatt MATH identifier: 1200.62059
Mathematical Reviews number (MathSciNet): MR2722464
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