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arXiv · 1202.5536

Detecting positive correlations in a multivariate sample

Ery Arias-Castro·Sébastien Bubeck·Gábor Lugosi
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Abstract

We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a general lower bound applicable to various classes and study the performance of some near-optimal tests. We pay special attention to computational feasibility and construct near-optimal tests that can be computed efficiently. Finally, we apply our results to prove new lower bounds for the clique number of high-dimensional random geometric graphs.

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Ery Arias-Castro, Sébastien Bubeck, Gábor Lugosi. 2015-04-14. Detecting positive correlations in a multivariate sample. https://doi.org/10.3150/13-bej565

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