Robustness Against Non-Normality : Evaluating LDA and QDA in Simulated Settings Using Multivariate Non-Normal Distributions

Abstract: Evaluating classifiers in controlled settings is essential for empirical applications, as extensive knowledge on model-behaviour is needed for accurate predictions. This thesis investigates robustness against non-normality of two prominent classifiers, LDA and QDA. Through simulation, errors in leave-one-out cross-validation are compared for data generated by different multivariate distributions, also controlling for covariance structures, class separation and sample sizes. Unexpectedly, the classifiers perform better on data generated by heavy-tailed symmetrical distributions than by the normal distribution. Possible explanations are proposed, but the cause remains unknown. There is need for further studies, investigating more settings as well as mathematical properties to verify and understand these results.