In the paper the theory of quadratic estimation of variance components in linear models and its applications are presented. In the presentation of the theory the coordinate-free approach is used. The applications concern estimation of variance components in general linear regression model and its special cases. The problem of admissibility of quadratic estimates in mixed linear models with two variance components is considered separately.
The paper includes uniformly most powerful unbiased test for a genetic model with two possible kinds of genes. This test is constructed on the basis of general theory of testing linear hypotheses for families of exponential distributions. An example of application for the system MN of blood-groups is given. Zbl 0465.62098; MR0549989
In the paper, the problem of estimation of variance components σ₁² and σ₂² by using the ML-method and REML-method in a normal mixed linear model 𝒩 {Y,E(Y) = Xβ, Cov(Y) = σ₁²V + σ₂²Iₙ} is considered. This paper deal with properties of estimators of variance components, particularly when an explicit form of these estimators is unknown. The conditions when the ML and REML estimators can be expressed in explicit forms are given, too. The simulation study for one-way classification unbalanced random...
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