A central question in multivariate data analysis is the number of factors, usually couched in terms of the "true" rank of the covariance matrix. A variety of optimality criteria can be applied to the sample covariance matrix; and these are in fact the basis for many standard multivariate inferential procedures including principal components analysis, factor analysis, multivariate analysis of variance and discriminant procedures. This research will examine various model selection methods, giving special attention to robustness. New approaches to discriminant analysis will be drawn using ideas from projection pursuit. Researchers analyzing observations on many variables simul- taneously face the problem of deciding how many factors are really important. The statistical procedures used to assess the e number of important factors needs to be stable in the presence of normal variation present in the data. This research focusses on desirable new methods to determine the number of such factors and also on methodology to identify interesting features in the data when many variables are observed at the same time for only a moderate number of individuals.
