Mathematical Geology

, Volume 25, Issue 5, pp 573-602

First online:

Euclidean Distance Matrix Analysis (EDMA): Estimation of mean form and mean form difference

  • Subhash LeleAffiliated withDepartment of Biostatistics, School of Hygiene and Public Health, The Johns Hopkins University

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Euclidean Distance Matrix Analysis (EDMA) of form is a coordinate free approach to the analysis of form using landmark data. In this paper, the problem of estimation of mean form, variance-covariance matrix, and mean form difference under the Gaussian perturbation model is considered using EDMA. The suggested estimators are based on the method of moments. They are shown to be consistent, that is as the sample size increases these estimators approach the true parameters. They are also shown to be computationally very simple. A method to improve their efficiency is suggested. Estimation in the presence of missing data is studied. In addition, it is shown that the superimposition method of estimation leads to incorrect mean form and variance-covariance structure.

Key words

coordinate free approach invariance principle moment estimators non-central chi-square nuisance parameters procrustes methods superimposition missing data