Open Access
February 2012 Detection of correlations
Ery Arias-Castro, Sébastien Bubeck, Gábor Lugosi
Ann. Statist. 40(1): 412-435 (February 2012). DOI: 10.1214/11-AOS964


We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a certain combinatorial structure known to the statistician. We establish upper and lower bounds for the worst-case (minimax) risk in terms of the size of the correlated subset, the level of correlation, and the structure of the class of possibly correlated sets. We show that some simple tests have near-optimal performance in many cases, while the generalized likelihood ratio test is suboptimal in some important cases.


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Ery Arias-Castro. Sébastien Bubeck. Gábor Lugosi. "Detection of correlations." Ann. Statist. 40 (1) 412 - 435, February 2012.


Published: February 2012
First available in Project Euclid: 16 April 2012

zbMATH: 1246.62142
MathSciNet: MR3014312
Digital Object Identifier: 10.1214/11-AOS964

Primary: 62F03
Secondary: 62F05

Keywords: Bayesian detection , Generalized likelihood ratio test , minimax detection , scan statistic , Sparse covariance matrix

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 1 • February 2012
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