Hocking, R.R.; Green, J.W.; Bremer, R.H. (1989, ASQC and the American Statistical Association) Texas A&M University, College Station, TX; University of Delaware, Newark, DE; Texas Tech University, Lubbock, TX
The problem of estimating variance components in mixed linear models has no satisfactory solution for the unbalanced data case. Further, there has been little work on diagnostic methods for assessing the data and the model. In this article, we propose a new class of unbiased estimators. These estimators have simple closed-form expressions allowing for small-sample analysis and easy computations. The structure of the estimators reveals natural diagnostics for examining the data and the model assumptions. The source of negative estimates of variance components is revealed. Limited efficiency studies indicate that these estimators are comparable to existing estimators. The estimators are illustrated by two numerical examples that reveal the importance of the diagnostic analysis.