Large scale correlation detection

This work addresses the problem of correlation detection in a group of elliptically-contoured variables, when the number p of variates greatly exceeds the number n of observed samples. We exploit the properties inherent to the Z-score representation of the data set to devise two different decision tests, whose performances are assessed by upper bounding the Type I and Type II error probabilities. The results specifically apply to the asymptotic regime where the number of variates p is large, and the number of samples n is finite and fixed.