Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure

The paper deals with the best unbiased estimators of the blocked compound symmetric covariance structure for mm-variate observations over uu sites under the assumption of multivariate 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. Complete statistics are then derived to prove that the estimators are best unbiased. Finally, strong consistency is proven. The proposed method is implemented with a real data set.