A general property among nested,pruned subtrees of a decision-support tree

Breiman, Friedman, Olshen, and Stone (1984) use a linear combination of prediction risk and tree size as a criterion in search of optimal trees. In this paper we use a linear combination of the above two components and the variable-observation cost as a criterion (C ₁) for the same purpose. This paper explicitly represents the relation among nested, pruned subtrees in terms of C ₁. Further, the theories in Breiman et al. (1984) concerning the search of optimal trees are generalized.