A Simple Test For The Independence of Sets of Variables

A test for the mutual independence of subvectors of the p-dimensional random vector X , distributed as N( 0, S? ), is described. The test is based on the maximum likelihood estimates (MLEs) of the off-(block) diagonal elements of S?. It is shown that the resulting test statistic is much easier to compute than the likelihood ratio (LR) test statistic while retaining the same asymptotic power properties in view of the general properties of tests based on the MLEs (ML test) and the likelihood ratio (LR test).