Comparison of Distance-Based Classifiers for Elliptically Contoured Distributions

A simulation study is carried out to compare three distance-based classifiers for their misclassification and asymptotic distributions when the data follow certain elliptically contoured distributions. The data are generated from multivariate normal, multivariate t and multivariate normal mixture distributions with varying covariance structures, sample sizes and dimension sizes. In many of the simulated cases, the dimensions of the data are much larger than the sample size. The simulations show that for small dimension sizes, the centroid classifier generally performs better. The nearest neighbour classifier shows superior performance compared to the other classifiers when the covariance structure is of compound symmetry form. All three classifiers showed to have asymptotic normal distribution, regardless of the underlying distribution of the data