Perturbation Theory for Generalized Procrustes Analysis
研究当两个配置都受独立正态误差影响时，Procrustes统计量的扰动理论，将总平方和分解为平移、旋转/反射和缩放的平方和加残差，并推广到广义Procrustes分析，为Gower的方差分析总结提供了理论依据。
SUMMARY Perturbation theory for Procrustes statistics is developed when both configurations are subject to independent normal errors. The total sum of squares is shown to partition into sums of squares for translation, rotation/reflection and scaling, plus a residual. These results are extended to generalized Procrustes analysis. This gives a theoretical justification to Gower's analysis of variance summary of the results from a generalized Procrustes analysis.