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arXiv · 0908.3437

On combinatorial testing problems

Louigi Addario-Berry·Nicolas Broutin·Luc Devroye·Gábor Lugosi
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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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Louigi Addario-Berry, Nicolas Broutin, Luc Devroye, Gábor Lugosi. 2009-08-24. On combinatorial testing problems. https://doi.org/10.1214/10-aos817

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