Journal ArticleDOI
ANOVA Models with Random Effects: An Approach via Symmetry
TLDR
The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry in this paper, and it is shown that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalized spectral decomposition.Abstract:
The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.read more
Citations
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Orthogonal partitions in designed experiments
TL;DR: A survey of the statistical theory of orthogonal partitions on a finite set is given in this paper, which includes Latin squares, semilattices of subgroups, and partitions defined by the ancestral subsets of a partially ordered set.
A bibliography on variance components an introduction and an update: 1984-2002
Hardeo Sahai,Anwer Khurshid +1 more
TL;DR: In particular, the study of variance through a class of linear models known as random and mixed models is a central topic in statistics with wide ramifications in both theory and applications as discussed by the authors.
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Factorial Dispersion Models
Terence P. Speed,R. A. Bailey +1 more
TL;DR: In this paper, a class of dispersion models for multi-indexed arrays of random variables is introduced and discussed, which generalize the second-order properties of variance component, randomization and exchangeability models, and lead naturally to general techniques for calculating the orthogonal decomposition, expected mean squares and other aspects of the analysis of variance of such arrays.
Journal ArticleDOI
Marginal permutation invariant covariance matrices with applications to linear models
TL;DR: In this article, the covariance structures in balanced linear models containing random factors which are invariant with respect to marginal permutations of the random factors are studied. But not every reparameterization keeps permutation invariance.
References
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Journal ArticleDOI
Cumulative Sum Charts
TL;DR: In this article, the development of process inspection schemes from the original methods of Shewhart to the new charts using cumulative sums, and surveys the present practice in the operation of schemes based on cumulative sums are presented.
Journal ArticleDOI
Discussion, Emphasizing the Connection Between Analysis of Variance and Spectrum Analysis*
TL;DR: In this paper, a classical analysis of variance, based on a pattern involving d observations in each of the r.c cells formed by crossing r rows with c columns, is studied.
Journal ArticleDOI
Generalized Wreath Products of Permutation Groups
Book
Group representations and applied probability
TL;DR: In this paper, the authors present an introduction to certain mathematical ideas which can be of considerable importance in applied probability and in statistical theory and assume some knowledge of the groups, though most concepts are defined below.