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.
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Langron et al. (1985) studied this question.
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