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Some Practical Aspects of Canonical Variate Analysis

 

作者: Norm A Campbell,  

 

期刊: Journal of Applied Statistics  (Taylor Available online 1979)
卷期: Volume 6, issue 1  

页码: 7-18

 

ISSN:0266-4763

 

年代: 1979

 

DOI:10.1080/02664767900000002

 

出版商: Sheffield City Polytechnic

 

关键词: Canonical variate analysis;shrunken estimators

 

数据来源: Taylor

 

摘要:

Canonical variate analysis can be viewed as a two-stage principal component analysis. Explicit consideration of the principal components from the first stage, formalized in the content of shrunken estimators, leads to a number of practical advantages. In morphometric studies, the first eigenvector is often a size vector, with the remaining vectors contrast or shape-type vectors, so that a decomposition of the canonical variates into size and shape components can be achieved. In applied studies, often a small number of the principal components effect most of the separation between groups; plots of group means and associated concentration ellipses (ideally these should be circular) for important principal components facilitate graphical inspection. Of considerable practical importance is the potential for improved stability of the estimated canonical vectors. When the between-groups sum of squares for a particular principal component is small, and the corresponding eigenvalue of the within-groups correlation matrix is also small, marked instability of the canonical vectors can be expected. The introduction of shrunken estimators, by adding shrinkage constrants to the eigenvalues, leads to more stable coefficients.

 

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