Detection of correlations
Ery Arias-Castro, Sébastien Bubeck, Gábor Lugosi
The Annals of Statistics · 2012 · Volume 40 · Issue 1
Abstract
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.
Keywords
62F03, 62F05, Bayesian detection, Generalized likelihood ratio test, minimax detection, scan statistic, Sparse covariance matrix
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