A study of the effect of kurtosis on discriminant analysis under elliptical populations

This paper is concerned with the role some parameters indexing four important families within the multivariate elliptically contoured distributions play as indicators of multivariate kurtosis. The problem is addressed for the exponential power family, for a subclass of the Kotz family and for the Pearson type II and type VII distributions. Once such a problem is analyzed, we study the effect these parameters have, as kurtosis indicators, on binary discriminant analysis by exploring their relationship with the error rate of the Bayes discriminant rule. The effect is analyzed under mild conditions on the kernel function generating the elliptical density. Some numerical examples are given in order to illustrate our theoretical insights and findings.