Direct variable selection for discrimination among several groups

We propose a criterion for variable selection in discriminant analysis. This criterion permits to arrange the variables in decreasing order of adequacy for discrimination, so that the variable selection problem reduces to that of the estimation of suitable permutation and dimensionality. Then, estimators for these parameters are proposed and the resulting method for selecting variables is shown to be consistent. In a simulation study, we compute proportions of correct classification after variable selection in order to gain understanding of the performance of our proposal and to compare it to existing methods.