Open Access
August 2002 Modeling through group invariance: an interesting example with potential applications
Heng Li
Ann. Statist. 30(4): 1069-1080 (August 2002). DOI: 10.1214/aos/1031689017


A particular linear group symmetry model, called the dyadic symmetry model, is studied in some detail. Statistical procedures analogous to (multivariate) analysis of variance are introduced. This model may be suitable for various kinds of data collected on pairs of sampling units. Examples include (complete) diallel cross experiments in genetics and social relations analysis in psychology, for which ad hoc methods of analysis have been developed independently in those disciplines.

Our approach is based entirely on formal data structure following the principle of group symmetry, and hence its applicability is not restricted to any specific substantive areas. This paper illustrates the benefits that can be derived from the exploration of mathematical meanings in the development of statistical methods.


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Heng Li. "Modeling through group invariance: an interesting example with potential applications." Ann. Statist. 30 (4) 1069 - 1080, August 2002.


Published: August 2002
First available in Project Euclid: 10 September 2002

zbMATH: 1101.62341
MathSciNet: MR1926168
Digital Object Identifier: 10.1214/aos/1031689017

Primary: 20C99 , 62A01 , 62E15 , 62H05 , 62J10 , 62P10 , 62P15

Keywords: Diallel cross , dyadic symmetry model , exchangeability , group symmetry model , linear group symmetry model , patterned covariance , social relations model

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 4 • August 2002
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