Titlebook: Optimum Designs for Multi-Factor Models; Rainer Schwabe Book 1996 Springer-Verlag New York, Inc. 1996 Factor.Partition.Variance.addition.d

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A Review on Optimum Design Theory useful tools for checking optimality (Subsection 2.2). We omit the proofs of these standard results since they have been presented extensively in the literature. In particular, we refer to the monographs by . (1972), . et al. (1977, 1980), . et al. (1983, 1987), . (1980), . (1986) and . (1993).

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Reduction Principlesesigns and which permit to search for an optimum design in a substantially smaller subclass. The first part of this section is devoted to tools which deal with reductions to subsystems of regression functions and, hence, to subsystems of parameters. In the second part a further inherent structure is

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Complete Product-type Interactionst first we treat the case of complete interactions which has been thoroughly investigated in the literature starting from . (1965). With respect to the methods of proof involved the present section is dedicated to the equivalence theorems which have been presented in Section 2.

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No Interactions problems in which product designs are optimum and, again, the associated marginal designs are optimum in the corresponding marginal models. In particular, .-optimality is included if there is a constant term in the model under consideration. Such additive models with an explicit constant term will

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Some Additional Resultswe will sketch the idea of conditional designs in the situation of one qualitative factor completely interacting with the second factor. These complete interaction structures will include the dependence of the conditional design region .(.) and the regression function . on .. Some hints on partial i

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