On combinatorial testing problems
Abstract
We study a class of hypothesis testing problems in which, upon observing the realization of an -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.
Cite
@article{arxiv.0908.3437,
title = {On combinatorial testing problems},
author = {Louigi Addario-Berry and Nicolas Broutin and Luc Devroye and Gábor Lugosi},
journal= {arXiv preprint arXiv:0908.3437},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOS817 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)