On combinatorial testing problems
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2009
 arXiv:
 arXiv:0908.3437
 Bibcode:
 2009arXiv0908.3437A
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Combinatorics
 EPrint:
 Published in at http://dx.doi.org/10.1214/10AOS817 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)