Forward and backward stepping in variable selection

This is the authors' abstract. We don't add key points for this paper.

For stepwise regression and discriminant analysis the parameters F in and F out govern the inclusion and deletion of variables. The candidate variable with the biggest F—ratio is included if this exceeds F inthe included variable with the smallest F—ratio is deleted if this is less than F in If F in ≧F out; then return to a previous subset size implies improvement in the criterion measure. This result also holds for a generalization, stepwise multivariate analysis, which includes stepwise regression and discriminant analysis as special cases Eliminations do not occur if forward regression and backward elimination yield the same sequence of subsets. Conversely, there is a more liberal stepping rule which always eliminates if the two sequences differ.