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

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1988

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