When product type experimental design is optimal? Brief survey and new results
type: Item
instance of: scholarly article
title: When product type experimental design is optimal? Brief survey and new results
zbMATH Open document ID: 0766.62046
DOI: 10.1007/BF02614014
published in: Metrika
publication date: 1993-04-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176433
review text: The authors considered a classical linear regression model and found conditions to be imposed and a criterion under which one can find an optimal design \(\xi\) in a certain class of designs. They considered product designs for multiplicative and additive multivariate models. A number of models, especially polynomial, polynomial plus trigonometric regression and mixed models have been considered and conditions for \(D\)-, \(L\)- and \(\psi\)-optimality, etc. have been derived. The authors have chosen very general models in vector and matrix form with Kronecker product notation and their applications in practical situations like factorial experiments have been shown as a particular case. This paper needs very good background in matrix theory.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62K15
zbMATH DE Number: 146906
zbMATH Keywords: multivariate regression
zbMATH Keywords: product designs
zbMATH Keywords: additive multivariate models
zbMATH Keywords: polynomial plus trigonometric regression
zbMATH Keywords: mixed models
author: Ewaryst Rafajłowicz
author: Wojciech Myszka
reviewed by: B. L. Agarwal
MaRDI profile type: Publication
cites work: Q4197800
cites work: Minimax Designs in Two Dimensional Regression
cites work: General equivalence theory for optimum designs (approximate theory)
cites work: Q5331504
cites work: Optimum experimental design for a regression on a hypercube- generalization of Hoel's result
cites work: A-optimal design measures for one-way layouts with additive regression
cites work: An application of the Kiefer-Wolfowitz equivalence theorem to ANOVA models with additive regression
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description: scientific article; zbMATH DE number 146906