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October 2010 On combinatorial testing problems
Louigi Addario-Berry, Nicolas Broutin, Luc Devroye, Gábor Lugosi
Ann. Statist. 38(5): 3063-3092 (October 2010). DOI: 10.1214/10-AOS817


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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Louigi Addario-Berry. Nicolas Broutin. Luc Devroye. Gábor Lugosi. "On combinatorial testing problems." Ann. Statist. 38 (5) 3063 - 3092, October 2010.


Published: October 2010
First available in Project Euclid: 30 August 2010

zbMATH: 1200.62059
MathSciNet: MR2722464
Digital Object Identifier: 10.1214/10-AOS817

Primary: 62F03
Secondary: 62F05

Keywords: Gaussian processes , Hypothesis testing , multiple hypotheses

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 5 • October 2010
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