Estimating the Expected Probability of Misclassification for a Rule Based on the Linear Discriminant Function: Univariate Normal Case

Abstract

The problem is to estimate the average probability of misclassifying an observation from a given population in the context of the two group classification problem when populations are univariate normal with unknown means and common known variance, and the rule is based on the linear discriminant function. Several estimators are compared with respect to asymptotic MSE and with respect to the distribution of the absolute error between estimator and parameter, and conclusions drawn about the best estimators.