Inequalities associated with intra–inter-class correlation matrices

This paper complements the results of Tong (Ann. Statist. 17 (1989) 429), Shaked and Tong (Ann. Statist. 20 (1992) 614) and Eaton (in: Stochastic Inequalities, IMS Lecture Notes Monograph Series, Vol. 22, 1993, 76) by deriving some monotonicity results associated with intra–inter-class correlation matrices. In Section 2, we consider the problem of comparing these matrices in terms of the orderings induced by several subgroups of the orthogonal group. Section 3 is devoted to deriving some probability inequalities for normal random variables whose correlation matrix is of the intra–inter-class correlation structure.