Modeling through group invariance: An interesting example with potential applications

• 成果类型: Article
• 署名作者: Li, H
• 署名单位: University of Rochester
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2002
• 页码: 1069-1080
• 关键词: maximum-likelihood-estimation; em algorithm; ASYMPTOTIC VARIANCE; ecm algorithm

摘要

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.