The Annals of Statistics

Modeling through group invariance: an interesting example with potential applications

Heng Li

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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.

Article information

Ann. Statist., Volume 30, Number 4 (2002), 1069-1080.

First available in Project Euclid: 10 September 2002

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Zentralblatt MATH identifier

Primary: 62H05: Characterization and structure theory 62J10: Analysis of variance and covariance 62A01: Foundations and philosophical topics 62E15: Exact distribution theory 20C99: None of the above, but in this section 62P15: Applications to psychology 62P10: Applications to biology and medical sciences

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


Li, Heng. Modeling through group invariance: an interesting example with potential applications. Ann. Statist. 30 (2002), no. 4, 1069--1080. doi:10.1214/aos/1031689017.

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