Principal components on coefficient of variation matrices

The coefficient of variation (CV) matrix for a pp-dimensional random vector is the covariance matrix scaled by the pp-vector of means such that the diagonal components are the squared coefficients of variation. In this article, principal component models for the CV matrix are proposed and least-squares estimators of the eigenvalues and eigenvectors are developed. The asymptotic joint distribution of the least-squares estimators is derived under general conditions. The proposed estimation and inference methods are illustrated using a real data set. The results of a small simulation study that examines the validity of the proposed inference procedures are reported.