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.
Citation
Ery Arias-Castro. Sébastien Bubeck. Gábor Lugosi. "Detecting positive correlations in a multivariate sample." Bernoulli 21 (1) 209 - 241, February 2015. https://doi.org/10.3150/13-BEJ565
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