Measures of Asociation between vectors

Let be a (p+q) - variate random vector (p≧1, q≧1) with . Partition ∑into p- and q- rows and columns such that . Let be the nonzero characteristic roots of where s is the rank of ∑12. Based on those roots, a class measures of association between is characterised. Some basic properties of these measures are explored. Among various special cases, an attractive measure of association is favoured which is derived from the vector coefficient of alienation. Justification fof the use of such a measure is included.