Robustness of the Fisher’s Discriminant Function to Skew-Curved Normal Distribution

Discriminant analysis is a widely used multivariate technique with Fisher’s discriminant analysis (FDA) being its most venerable form. FDA assumes equality of population covariance matrices, but does not require multivariate normality. Nevertheless, the latter is desirable for optimal classification. To test FDA's performance under non-normality caused by skewness the method was assessed with simulation based on a skew-curved normal (SCN) distribution belonging to the family of skew-generalised normal distributions; additionally, effects of sample size and rotation were evaluated. Apparent error rate (APER) was used as the measure of classification performance. The analysis was performed using ANOVA with (transformed) mean APER as the dependent variable. Results show the FDA to be highly robust to skewness introduced into the model via the SCN distributed simulated data.