Abstract
This paper investigates the robustness properties of linear discriminant analysis. We study the problem distorting the assumptions of the linear discriminant rule that the populations are normally distributed and they have equal variance and covariance matrices. Assuming that the populations are lognormally distributed and they have equal or unequal variance and covariance matrices, we investigate the robustness of validity and the robustness of efficiency of the rule. In the case of one dimension, we obtain the asymptotic expansion of the misclassification probability and the risk of classification rule, and we investigate the robustness properties using approximate probabilities. In the case of more than one dimension, we investigate them using Monte Carlo simulation.
