Data driven choice of the classification rule in discriminant analysis applied to isoberlinia stands

A simulation study is performed to evaluate, in discriminant analysis, the relative performance of the linear, quadratic and logistic rules, on 52,800 sample couples, characterized by the distribution and the overlap of the populations, the number of variables, the samples size and the theoretical heteroscedasticity degree of the populations, defined in the study. For each sample couple, the relative error of the actual error rate of each classification rule is computed as well as the estimated heteroscedasticity degree and the multinormality test's statistic. The results obtained helps to notice that the linear rule can be advised when the multinormality hypothesis is accepted and the logistic rule in the other cases. The quadratic rule gives the lowest performance in most of the considered cases. Anoter method is based on the estimated heteroscedasticity and normality degrees of the considered sample couple.