Consistency of split-complexity pruning

Establish whether split-complexity pruning of the kernel dipole-splitting survival tree induces an asymptotic regime in which the clinical-stage cumulative-hazard estimator is consistent, thereby validating the consistency hypothesis required by Theorem 1.

Background

The theoretical residual-separation result assumes that the clinical survival tree consistently estimates the covariate-conditional cumulative hazard. Remark 1 explains that the default stopping rule, which prevents children from falling below a fixed minimum size, can produce leaves whose sample sizes do not increase with the total sample size; consequently, leaf-level Nelson–Aalen estimates need not converge. The paper therefore assumes a regime in which the tree partition stabilizes and leaf sample sizes grow, rather than proving that the implemented procedure enters such a regime.

The paper specifically identifies the unresolved issue as whether the split-complexity pruning procedure described in Section 3.3 can induce the required asymptotic behavior. Resolving this question would provide a formal consistency foundation for the clinical stage and strengthen the theoretical justification of the two-stage spatial-risk procedure.