Comparison of Parametric and Empirical Estimators of Misclassification Rates in Discriminant Analysis

• Activity Number: 561
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Alice Hinton*+ and Haikady Nagaraja
• Companies: and Ohio State University
• Keywords: Discriminant Analysis ; Estimation ; Multivariate Normal Distribution

Abstract

Discriminant functions are developed to classify a new observation from a cross-sectional dataset into a population. An error is made when the observation is incorrectly classified. In the literature, several parametric and empirical methods of estimating these misclassification probabilities have been proposed. The performance of six parametric and three empirical misclassification probability estimators are compared. It is found that the parametric methods, which rely on an assumption of normality, generally outperform the empirical methods when a linear discriminant function is used for classification and the data originate from normal populations. The preferred parametric method depends on the size of the training dataset and the parameters of the populations, particularly the distance between the means. The empirical methods are preferred only when the two populations are well separated and the variances are significantly different.