Canonical Discriminant Analysis: Comparison of Resampling Methods and Convex-Hull Approximation

Abstract

The predictive power of Canonical Discriminant Analysis is examined by means of variants of the delete-p%-jackknife, the bootstrap, and convex-hull approximation. Characteristics of predictive power are based upon estimated tolerance regions of the different classes of observations in that the coverage of the regions is investigated and one kind of misclassification rates is based upon these regions. Additionally, misclassification rates based upon densities are examined. Simulation data basically consist of 3 clusters of points in 2 dimensions with various distributional properties. The results indicate the superiority of those methods with the most varying samples, i.e. the delete- 10%/50%-jackknife and the bootstrap, to set up prediction rules. Concerning misclassification rates convex-hull approximation of tolerance regions appeared to be competitive. Convex-hull approximation did not lead to a distinct improvement in case of non-normal data. For the characterization of predictive power, the misclassification rate based upon densities should be prefered.