Free-coordinate estimation for doubly multivariate data

The article addresses the best unbiased estimators of the block compound symmetric covariance structure for m−variate observations with equal mean vector over u sites under the assumption of multivariate quasi-normality. The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matrices. Without assumption of normality but quasi-normality, meaning that up to fourth moments are the same as in the normal case, the estimators are best linear and best quadratic for mean and covariance parameters, respectively. Finally, strong consistency is proven. The properties of the estimators in the proposed model are compared against a similar model available in the literature. An application of the proposed approach to a clinical study data is presented.