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Cumulants and partition lattices VI. variances and covariances of mean squares

Part of: Linear inference, regression

Published online by Cambridge University Press:  09 April 2009

T. P. Speed  and
H. L. Silcock
T. P. Speed
Affiliation:
Division of Mathematics and StatisticsCSIRO Canberra 2601, Australia
H. L. Silcock
Affiliation:
Division of Mathematics and StatisticsCSIRO Canberra 2601, Australia
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Abstract

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Formulae are given for the variances and covariances for mean squares in anova under the broadest possible assumptions. The results of ther authors are obtained by specializing appropriately: these include ones concerning randomization and/or random sampling models, as well as additive (linear) models consisting of mutually independent sets of exchangeable effects. Although the illustrations given refer only to doubly and triply-indexed arrays, the approach is quite general. Particular attention is drawn to the generalized cumulants (and their natural unbiased estimators) which vanish when additive models are assumed.

Keywords

cumulantk-statisticanova modelcomponent of variancedesigned experimenttreatment mean squarerandomization.

MSC classification

Secondary: 62J10: Analysis of variance and covariance
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 3 , June 1988 , pp. 362 - 388
Copyright
Copyright © Australian Mathematical Society 1988

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