PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Detection of correlations
Ery Arias-Castro, Sébastien Bubeck and Gábor Lugosi
Annals of Statistics Volume to appear, 2011.


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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:7643
Deposited By:Gábor Lugosi
Deposited On:21 February 2012