Complex linear models and cyclic designs
type: Item
instance of: scholarly article
title: Complex linear models and cyclic designs
zbMATH Open document ID: 0733.62080
DOI: 10.1016/0024-3795(90)90344-C
author: André Kobilinsky
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: Abelian group theory has been used to construct many orthogonal fractional replicates or block designs in confounding. Usually, abelian group structures are given to the set of experimental units, the set of treatments, and, for block designs, the set of blocks. The mapping assigning a treatment, or a block, to each experimental unit is then chosen among affine mappings, which are the composition of a group morphism and a translation. In this energetic paper, several concepts of designs and properties are discussed systematically. From the abstract: ``Many orthogonal factorial designs can be defined by abelian group morphisms. By juxtaposition of such designs, useful nonorthogonal designs can also be obtained, including the classical generalized cyclic designs, as well as a new kind of replicate factorial block designs. Their efficiencies are easily computed by means of a complex reparametrization based on the irreducible characters of the groups involved. The theory extends to the ``group generated designs'' defined by \textit{R. A. Bailey} and \textit{C. A. Rowley} [ibid., 183-225 (1990; Zbl 0725.62067)] where the group is not necessarily abelian. In some cases, we give explicit formulas for the efficiencies of these latter designs.''
reviewed by: Sanpei Kageyama
Mathematics Subject Classification ID: 62K15
Mathematics Subject Classification ID: 20K99
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 20K30
zbMATH DE Number: 4213270
zbMATH Keywords: orthogonal fractional replicates
zbMATH Keywords: confounding
zbMATH Keywords: affine mappings
zbMATH Keywords: orthogonal factorial designs
zbMATH Keywords: abelian group morphisms
zbMATH Keywords: juxtaposition
zbMATH Keywords: nonorthogonal designs
zbMATH Keywords: generalized cyclic designs
zbMATH Keywords: replicate factorial block designs
zbMATH Keywords: efficiencies
zbMATH Keywords: complex reparametrization
zbMATH Keywords: irreducible characters
zbMATH Keywords: group generated designs
MaRDI profile type: Publication
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full work available at URL: 0024-3795(90)90344-c
OpenAlex ID: W2085329133
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description: scientific article; zbMATH DE number 4213270