Influence measures for multivariate analysis

The purpose of this dissertation is to suggest two measures of influence for use in the multivariate analysis techniques of linear discriminate analysis and cluster analysis. Both of these influence measures have been developed for normal data and both compare the estimated volumes of the convex hulls about the groups or clusters for the full and reduced data sets. The first measure of influence compares the product of volumes of the confidence ellipsoids about the group or cluster means for the full and reduced data sets and the second measure of influence compares the sum of the volumes of the confidence ellipsoids for the full and reduced data sets. These two influence measures are, for computational purposes, developed by using a multivariate linear regression model which represents the linear discriminate analysis or cluster analysis problem.;For both influence measures, bounds are derived which are useful for labelling influential points. Simulation studies and examples are presented.