Assessing large sets of rank correlations

Abstract

A recent Poisson limit theorem for dissociated random variables is shown to apply to rank correlation coefficients which have been calculated from independently distributed vectors. This allows the asymptotic distribution of the largest of the rank correlations to be derived. Simulations show that the asymptotic approximations are close in the tails of the distributions. An example indicates how these approximations can be used to assess the significance of the large correlation coefficients.