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Extreme shape analysis
Author(s) -
Dryden Ian L.,
Zempléni András
Publication year - 2006
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2005.00533.x
Subject(s) - estimator , inference , mathematics , maximum likelihood , bounded function , extreme point , statistics , algorithm , computer science , combinatorics , artificial intelligence , mathematical analysis
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.