By H. Sahai, M. Ojeda
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Additional resources for Analysis of Variance for Random Models [Vol II - Unbalanced Data]
Proof. 26), we note that λ = S− , so that λ exists if an unbiased estimator of i=1 i σi2 exists. 26). Now, let p 46 Chapter 10. Making Inferences about Variance Components A = A∗ + D be an alternative matrix. Then tr[DVi ] = 0, i = 1, . . , p. Furthermore, DX = 0 → RH D = D. Then p ∗ tr[A H DH ] = λi tr[RVi RH DH ] i=1 p λi tr[Vi DH R] = i=1 p λi tr[Vi D] = i=1 = 0.
3 Chapter 10. Making Inferences about Variance Components HENDERSON’S METHOD III The procedure known as Henderson’s Method III uses reductions in sums of squares due to ﬁtting constants (due to ﬁtting different models and submodels) in place of the analysis of variance sums of squares used in Methods I and II using a complete least squares analysis. Thus it is also commonly referred to as the method of ﬁtting constants. We have seen that for ﬁxed effects, having normal equations X Xβ = X Y , the reduction in sum of squares due to β, denoted by R(β), is R(β) = Y X(X X)− X Y .
Making Inferences about Variance Components (1977a, 1977b) discussed the application of the ML procedure for the estimation of heritability. 1. As pointed out by Harville (1969a), however, there are several drawbacks of the Hartley and Rao procedure. Some of them are as follow: (i) Though it produces a solution to the likelihood equations, over the constrained parameter space, there is no guarantee that the solution is an absolute maximum of the likelihood function over that space. (ii) While it is true that the procedure yields a sequence estimator with the usual asymptotic properties of maximum likelihood estimators, it is hard to justify the choice of an estimator on the basis of its being a part of a “good’’ sequence.
Analysis of Variance for Random Models [Vol II - Unbalanced Data] by H. Sahai, M. Ojeda