Abstract
In this chapter we investigate the effect of Generalized Procrustes Analysis (GPA) superimposition on the power of NonParametric Combination (NPC) testing methodology. Through a simulation study, we show how GPA alters power function. Since GPA superimposition provides permutationally non-equivalent transformations, NPC tests are approximate. Moreover, we examine the case of correlated landmarks. Through a toy example, considering hypothetical configurations representing some 3D monkey skulls, we compare the behavior of traditional tests with that of nonparametric permutation tests in this particular case. Finally we introduce paired data problem that, in the context of shape analysis, relates to the study of symmetric structures. Inferential techniques for symmetric shapes are presented.
“We call a thing big or little with reference to what it is wont to be, as we speak of a small elephant or a big rat.”.
On Growth and Form, 1917D’
Arcy Thompson
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Brombin, C., Salmaso, L. (2013). Evaluating Power Behavior of Nonparametric Combination Testing Methodology After Generalized Procrustes Analysis and Under Different Correlation Structures. In: Permutation Tests in Shape Analysis. SpringerBriefs in Statistics, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8163-8_3
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DOI: https://doi.org/10.1007/978-1-4614-8163-8_3
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