Equi-covariable Composite – A Connection to Equal-row-sum Covariance Matrix

Abstract

The concept of a class of equi-covariable composites (EC class) is introduced when the multivariate data are the outcomes of a repeated-measurement experiment as appears frequently in psychometric, biometric or social studies. Along with interesting properties of such class, the distinction between the generator (generating the EC class) and the best linear unbiased estimator (BLUE), introduced by C.R. Rao, is pointed out. Surprisingly, when the average of the variables belongs to all EC class the covariance matrix (Σ) of the associated variables should maintain equal row (or column) sums (ERS). Possibility of an extended EC class by sequential augmentation of new variables could arise when Σ would have “stair-case” ERS structure which maintains ERS property right from first variable through the last variable.