The Annals of Statistics

On combinatorial testing problems

Louigi Addario-Berry, Nicolas Broutin, Luc Devroye, and Gábor Lugosi

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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.

Article information

Ann. Statist., Volume 38, Number 5 (2010), 3063-3092.

First available in Project Euclid: 30 August 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F03: Hypothesis testing
Secondary: 62F05: Asymptotic properties of tests

Hypothesis testing multiple hypotheses Gaussian processes


Addario-Berry, Louigi; Broutin, Nicolas; Devroye, Luc; Lugosi, Gábor. On combinatorial testing problems. Ann. Statist. 38 (2010), no. 5, 3063--3092. doi:10.1214/10-AOS817.

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