“The discusssion below (20) for variance estimation and in the Appendix B seems to be heuristic. If the arguments could be made (more) rigorous, then it would be helpful to do so. Otherwise, it would be helpful to acknowledge the heuristic nature of the discussion, and pose as an open theoretical problem to fully address the convergence and variance estimation.”
In fact, the first sentence of our Appendix B is “To establish a heuristic argument for consistency of the INS scheme … “. Seems like we’re acknowledging the heuristic nature of our arguments and leaving open the theoretical problem for a strong proof. We also discuss the difficulties of the ongoing work to this end for the related problem of rigorously establishing consistency of the AMIS estimator.