On variance of the two-stage estimator in variance-covariance components model

summary:The paper deals with a linear model with linear variance-covariance structure, where the linear function of the parameter of expectation is to be estimated. The two-stage estimator is based on the observation of the vector $Y$ and on the invariant quadratic estimator of the variance-covariance components. Under the assumption of symmetry of the distribution and existence of finite moments up to the tenth order, an approach to determining the upper bound for the difference in variances of the estimators is proposed, which uses the estimated covariance matrix instead of the real one