Open Access
February 2015 Detecting positive correlations in a multivariate sample
Ery Arias-Castro, Sébastien Bubeck, Gábor Lugosi
Bernoulli 21(1): 209-241 (February 2015). DOI: 10.3150/13-BEJ565


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. "Detecting positive correlations in a multivariate sample." Bernoulli 21 (1) 209 - 241, February 2015.


Published: February 2015
First available in Project Euclid: 17 March 2015

zbMATH: 1359.62208
MathSciNet: MR3322317
Digital Object Identifier: 10.3150/13-BEJ565

Keywords: Bayesian detection , High-dimensional data , minimax detection , Random geometric graphs , Sparse covariance matrix , sparse detection

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 1 • February 2015
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