On estimation of variance components with constraints

Abstract

The so-called linear approach to estimating linear functions of variance and/or covariance components clearly shows the well-known connection between quadratic, invariant and unbiased, estimation and the classical linear theory methods, LSE and BLUE. This approach allows us to consider and to use further results of the linear theory for variance-covariance components estimation. In the present paper the minimax invariant quadratic estimators of linear functions of variance-covariance components under full or partial restrictions on the parameter set are investigated.