Some results on vector correlation

A measure of multivariate association between two sets of variables is examined. This is shown to be equivalent to a simple correlation coefficient between new variables obtained by transforming the original vectors. The measure is also shown to be asymptotically equivalent to a simple correlation coefficient between certain other variables. Some asymptotic distributions are obtained and simulations are carried out in order to determine whether these give reasonable approximations for finite sample sizes. Finally some suggestions are made for practical inference purposes.