Extreme shape analysis

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 mo...

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Bibliographic Details
Published in:Applied statistics 2006-01, Vol.55 (1), p.103-121
Main Authors: Dryden, Ian L., Zempléni, András
Format: Article
Language:English
Subjects:
Anatomy & physiology
Applications
Delaunay triangles
Deoxyribonucleic acid
Distribution
Distribution functions
DNA
Dynamic models
Estimators
Exact sciences and technology
Extreme value theory
Generalized Pareto distribution
Geometric shapes
Global analysis, analysis on manifolds
Inference
Linear inference, regression
Mathematics
Maximum likelihood estimation
Maximum likelihood estimators
Medical research
Methodology
Molecular dynamics
Muscle fibers
Muscles
Parametric inference
Peaks over threshold
Point estimators
Probability and statistics
Procrustes analysis
Procrustes distance
Return levels
Sciences and techniques of general use
Shape analysis
Shape space
Sphere
Statistical analysis
Statistical methods
Statistical models
Statistics
Studies
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Triangulation
Value analysis
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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.
ISSN:0035-9254
1467-9876
DOI:10.1111/j.1467-9876.2005.00533.x