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

Euclidean Distance Matrix Analysis (EDMA) of form is a coordinate free approach to the analysis o f form using landmark data. In this paper, the problem of estimation of mean form, variancecovariance 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.