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2012

Detecting positive correlations in a multivariate sample

Arias-Castro, Ery, Bubeck, Sébastien, Lugosi, Gábor

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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.

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