Nonparametric Confidence and Tolerance Regions in Canonical Variate Analysis

Abstract

Canonical variate analysis is a much-used descriptive multivariate technique for grouped data in which the group means are represented by points in a low- (typically two-) dimensional space. If inferential use is to be made of the technique some knowledge of the variability of these points under repeated sampling is necessary. The traditional approach is to construct confidence or tolerance circles around each point by using approximate asymptotic results based on normal assumptions for the data. Jackknife and bootstrap resampling schemes are proposed in this paper as a basis for constructing nonparametric regions. These regions are compared with the normal-based circles on the well-known Fisher Iris data, and also by means of a small Monte Carlo study incorporating nonnormal as well as normal data. It is suggested that the normal-based circles may often be inappropriate, and areas of further investigation are identified.