Complete a forest structure

Completes the forest in the sens of the Reference: adds the missing atoms/leafs in the reference family with a forest structure \((R_k, \zeta_k)\) so that each atom is well represented by a \(R_k\). The associated \(\zeta_k\) is taken as the trivial \(|R_k|\).

Usage

forest.completion(C, ZL, leaf_list)

Arguments

C

A list of list representing the forest structure. See V.star() for more information.

ZL

A list of integer vectors representing the upper bounds \(\zeta_k\) of the forest structure. See V.star() for more information.

leaf_list

A list of vectors representing the atoms of the forest structure. See V.star() for more information.

Value

A list with two named elements.

C

The new C after completion.

ZL

The new ZL after completion.

Details

The forest must not be pruned (with pruning()) beforehand. The code will not behave expectedly and will return a wrong result if a pruned forest is given as input. Maybe the function could be rewritten going from the leaves to the roots instead of the contrary, to avoid this issue.

References

Durand, G., Blanchard, G., Neuvial, P., & Roquain, E. (2020). Post hoc false positive control for structured hypotheses. Scandinavian Journal of Statistics, 47(4), 1114-1148.

Durand G. (2025). A fast algorithm to compute a curve of confidence upper bounds for the False Discovery Proportion using a reference family with a forest structure. arXiv:2502.03849.