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Extreme shape analysis

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  • Ian L. Dryden
  • András Zempléni

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.

Suggested Citation

  • Ian L. Dryden & András Zempléni, 2006. "Extreme shape analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(1), pages 103-121, January.
    • Handle: RePEc:bla:jorssc:v:55:y:2006:i:1:p:103-121
    DOI: 10.1111/j.1467-9876.2005.00533.x
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    Cited by:

    1. Irene Epifanio & María Victoria Ibáñez & Amelia Simó, 2018. "Archetypal shapes based on landmarks and extension to handle missing data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 705-735, September.

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