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ON COMBINATORIAL TESTING PROBLEMS
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DOI：10.1214/10-AOS817.png)
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Abstract
En 中文
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.
Keywords:
Hypothesis testing
multiple hypotheses
Gaussian processes
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