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On Confidence Regions in Canonical Variate Analysis
典型变量分析中的置信区域
It is argued that confidence circles as traditionally drawn on canonical variate diagrams are incorrect, because no allowance is made in their construction for the sampling variability of the canonical variate axes. A series of approximations is employed to obtain tractable expressions for the correct regions. Despite the rather broad approximations involved, empirical assessment via bootstrapping shows the new regions to have much more accurate probability content than the…
On confidence regions in canonical variate analysis
典型变量分析中的置信区域
It is argued that confidence circles as traditionally drawn on canonical variate diagrams are incorrect, because no allowance is made in their construction for the sampling variability of the canonical variate axes. A series of approximations is employed to obtain tractable expressions for the correct regions. Despite the rather broad approximations involved, empirical assessment via bootstrapping shows the new regions to have much more accurate probability content than the…
Sensitivity of Principal Components
主成分的敏感性
SUMMARY Simple analytical expressions are derived for the maximum changes in the coefficients of any principal component that are associated with a given (small) change in the variance of the component. This enables a sensitivity analysis to be conducted simultaneously with any principal component analysis, to investigate the stability of the derived components. This has implications for the interpretation of any set of components. A brief illustration is provided, and…
Between-Groups Comparison of Principal Components
组间主成分比较
A method is given for comparing principal component analyses conducted on the same variables in two different groups of individuals, and an extension to the case of more than two groups is outlined. The technique leads to a latent root and vector problem, which has also arisen in the comparison of factor patterns in separate factor analyses. Emphasis in the present article is on the underlying geometry and interpretation of the results. An illustrative example is provided.
Discrimination and Classification Using Both Binary and Continuous Variables
同时使用二元变量与连续变量的判别和分类
The likelihood ratio classification rule is derived from the location model, applicable when the data contains both binary and continuous variables. A method is proposed for estimating the rule in practical situations and assessing its performance. Losses incurred by the estimation procedure are investigated, and use of Fisher's linear discriminant function on such data is studied for the case of known population parameters. Finally, the proposed rule is applied to some data…