THE NONNEGATIVE OPTIMALITY OF LINEAR MODELS

This paper deals with the nonnegative unbiased estimability of variance components and gives a nonnegative optimality criterion for linear models. The Theorem 2. 1 extends the main result in （6）. The nonnegative optimality criterion of linear models is as follows: \left(Y, X \beta, \sum_i=1^k V_i \theta_i\right) is a given model, θ=（θ₁, …θ_k）Θ∈ \Theta=\left\\theta \in R^k \sum_i=1^k V_i \theta_i \geqslant 0\right\. Let α be an arbitrary prior value such that \sum_i=1^k V_i \alpha_i \geqslant 0.. If for each nonnegative estimable linear combination of variance components its MINQE_U,I is semi-definite, we say that the model has nonnegtive optimality. By using the theorem 2. 1, the nonnegative optimality of some random models commonly used are checked.