Abstract
We now begin the return to our statistical origins, by applying the algebraic techniques of the last two chapters to our variance component problem. Thus 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 of the space of optimal estimates is an invariant UMVUE.
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© 1986 Springer-Verlag Berlin Heidelberg
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Malley, J.D. (1986). The Algebraic Structure of Variance Components. In: Optimal Unbiased Estimation of Variance Components. Lecture Notes in Statistics, vol 39. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7554-2_9
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DOI: https://doi.org/10.1007/978-1-4615-7554-2_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96449-2
Online ISBN: 978-1-4615-7554-2
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