The two-group discriminant problem with equal group mean vectors: An experimental evaluation of six linear/nonlinear programming formulations

Various parametric and nonparametric approaches to multiple discriminant analysis attempt to discriminate among or classify entities (e.g. loan applicants, customers, employees, businesses) based on several of their distinguishing characteristics called discriminant variables. Statistical parametric procedures require that the mean vectors of discriminant variables for the populations of entities be different across groups. This requirement may not always be met in practical settings. This paper reports on a preliminary Monte Carlo simulation experiment which compares the performance of six 1p-norm distance models including two linear and four nonlinear formulations as well as two statistical procedures to address the discriminant problem under equal mean vectors. The experimental data were generated from multivariate normal or nonnormal populations with equal or unequal dispersion matrices and with or without outliers. The results indicate that, when population mean vectors are equal, the most significant characteristic which affects the performance of all of the methods is the similarity (or dissimilarity) of dispersion matrices. The departure from normality and the presence of outliers and some of the interactions between these three factors are also statistically significant.