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Consistency of Procrustes Estimators

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  • John T. Kent
  • Kanti V. Mardia

Abstract

Lele has shown that the Procrustes estimator of form is inconsistent and raised the question about the consistency of the Procrustes estimator of shape. In this paper the consistency of estimators of form and shape is studied under various assumptions. In particular, it is shown that the Procrustes estimator of shape is consistent under the assumption of an isotropic error distribution and that consistency breaks down if the assumption of isotropy is relaxed. The relevance of these results for practical shape analysis is discussed. As a by‐product, some new results are derived for the offset uniform distribution from directional data.

Suggested Citation

  • John T. Kent & Kanti V. Mardia, 1997. "Consistency of Procrustes Estimators," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 281-290.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:1:p:281-290
    DOI: 10.1111/1467-9868.00069
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    Cited by:

    1. Fabian J.E. Telschow & Michael R. Pierrynowski & Stephan F. Huckemann, 2021. "Functional inference on rotational curves under sample‐specific group actions and identification of human gait," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1256-1276, December.
    2. Farag Shuweihdi & Charles C. Taylor & Arief Gusnanto, 2017. "Classification of form under heterogeneity and non-isotropic errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1495-1508, June.
    3. Douglas L Theobald & Deborah S Wuttke, 2008. "Accurate Structural Correlations from Maximum Likelihood Superpositions," PLOS Computational Biology, Public Library of Science, vol. 4(2), pages 1-8, February.
    4. Alshabani, A.K.S. & Dryden, I.L. & Litton, C.D., 2007. "Partial size-and-shape distributions," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1988-2001, November.

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