• Bernoulli
  • Volume 21, Number 1 (2015), 209-241.

Detecting positive correlations in a multivariate sample

Ery Arias-Castro, Sébastien Bubeck, and Gábor Lugosi

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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. Finally, we apply our results to prove new lower bounds for the clique number of high-dimensional random geometric graphs.

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Bernoulli, Volume 21, Number 1 (2015), 209-241.

First available in Project Euclid: 17 March 2015

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Bayesian detection high-dimensional data minimax detection random geometric graphs sparse covariance matrix sparse detection


Arias-Castro, Ery; Bubeck, Sébastien; Lugosi, Gábor. Detecting positive correlations in a multivariate sample. Bernoulli 21 (2015), no. 1, 209--241. doi:10.3150/13-BEJ565.

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