Consistency and bootstrap coverage for cGNF estimators

Establish whether causal-graphical normalizing flow (cGNF) estimators provide consistent point estimates and whether bootstrap confidence intervals constructed from cGNF-based estimates achieve asymptotically valid coverage rates.

Background

The paper introduces cGNFs, which model the full joint distribution implied by a DAG using unconstrained monotonic neural networks and then estimate causal effects via Monte Carlo sampling. While simulations suggest good empirical performance, the authors note the absence of formal asymptotic guarantees for cGNF-based estimators and their bootstrap intervals. Formal results are necessary to underpin statistical inference based on cGNFs, such as consistency of point estimates and valid coverage of intervals.