Extreme shape analysis |
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Authors: | Ian L. Dryden, Andrá s Zemplé ni |
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Affiliation: | University of Nottingham, UK; Eötvös Loránd University, Budapest, Hungary |
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Abstract: | Summary. We consider the analysis of extreme shapes rather than the more usual mean- and variance-based shape analysis. In particular, we consider extreme shape analysis in two applications: human muscle fibre images, where we compare healthy and diseased muscles, and temporal sequences of DNA shapes from molecular dynamics simulations. One feature of the shape space is that it is bounded, so we consider estimators which use prior knowledge of the upper bound when present. Peaks-over-threshold methods and maximum-likelihood-based inference are used. We introduce fixed end point and constrained maximum likelihood estimators, and we discuss their asymptotic properties for large samples. It is shown that in some cases the constrained estimators have half the mean-square error of the unconstrained maximum likelihood estimators. The new estimators are applied to the muscle and DNA data, and practical conclusions are given. |
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Keywords: | Delaunay triangles DNA Extreme value theory Generalized Pareto distribution Molecular dynamics Muscles Peaks over threshold Procrustes analysis Procrustes distance Return levels Shape analysis Shape space Sphere |
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