Parametric and kernel density methods in discriminant analysis: Another comparison

AbstractComparisons of parametric and nonparametric approaches to discriminant analysis have been reported in which the kernel density method was surprisingly superior to conventional methods such as the linear discriminant function under conditions of normality. The assumptions underlying these comparisons, particularly those of independence, and their implications for product kernel methods are critically examined. A new comparison is made allowing for correlation. It is found that for independent or modestly positively correlated variables, the kernel method is superior to conventional parametric methods unadjusted for the particular correlation structure. With other correlation structures, however, the kernel method behaves erratically and may give poor classification or poor estimation of odds or both depending on the underlying parametric configuration