Estimation of Misclassification Rates in Discriminant Analysis with Normal Populations

• Activity Number: 643
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Alice Hinton*+ and Haikady Nagaraja
• Companies: The Ohio State University and The Ohio State University
• Keywords: Discriminant Analysis ; Multivariate Normal Distribution ; Estimation

Abstract

The resubstitution method of estimating misclassification rates in linear discriminant analysis is compared with the holdout method using holdout samples of sizes 1, 2, and 3. The comparison is carried out for a range of effect sizes as well as sizes of the training dataset. Furthermore, the distribution of the observations in the training dataset into the two populations is varied from an equal number of observations in each of the two populations to one population being much more heavily represented than the other. It is found that the preferred estimator, according to the mean squared error, is dependent on both the effect size and the size of the training dataset; the distribution of the observations in the training dataset has little effect on the final recommendations. The resubstitution method, while generally underestimating the misclassification rates, is preferred for smaller effect sizes, and for moderate effect sizes with small training datasets.