Detection of correlations

Details Detection of correlations Detection of correlations

2011-06-06

arxiv.org/abs/1106.1193v1

Mathematics

Statistics Theory

Scientific paper

We consider the hypothesis testing problem of deciding whether an observed high-dimensional normal vector has independent 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 Bayes 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 settings, while the generalized likelihood ratio test is suboptimal in some important cases.

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