Titlebook: Optimal Unbiased Estimation of Variance Components; James D. Malley Book 1986 Springer-Verlag Berlin Heidelberg 1986 Algebraic structure.C

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The Basic Model and The Estimation Problem,del. Then we state the essential estimation problem. Relationships among a constellation of possible estimation criteria are next studied, and finally an ordered combination of these key ideas is taken as the focus of our unbiased theory. In Chapter Ten we will look at a new combination of criteria

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Basic Linear Technique,, a subject we take up in the next chapter. The notions of vec, mat., I., tensor products ⊗, and some relations between them are discussed. Next are the space of symmetric matrices, its natural inner product, and a useful projection lemma.

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Linearization of the Basic Model,ter organization for the statement of the model, and of allowing us to apply where possible the large body of technique available for the linear model. We also present an alternative linearization of the basic model.

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The Seely-Zyskind Results,ruly general solutions to optimal estimation of variance components. This is accomplished through a careful presentation of results which were developed in a series of papers by Justus Seely and George Zyskind: Zyskind [1967], Seely [1971], and Seely and Zyskind [1971]. Then at the end of the chapte

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Background from Algebra,. We have made an effort to keep the definitions to the minimum needed for an adequate description of this structure theory. Examples have been collected from the statistical literature which have a nontrivial algebraic content, but which may not have been appreciated as such by many readers.

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The Algebraic Structure of Variance Components,hus after showing that the space of optimal kernels is, in the kurtosis zero case, a semisimple Jordan algebra, we can invoke the First and Second Structure Theorems of Chapter 8, and this in turn will have purely statistical consequences as shown in Chapter 10. We also briefly examine when a member