# On variance estimation of the inverse probability-of-treatment weighting estimator#

What is the variance of the IPTW estimator when taking into account the estimation step ?

## Motivation#

We should take into account the variance from the two steps of the IPTW estimator : the estimation of the propensity score (treatment probabilities) and the estimation of the treatment effect by reweighting the outcome.

😍 *Non-parametric bootstrap can be used to obtain valid SEs, but the bootstrap may be computationally intensive for large databases.* So, the authors are concerned with analytical approaches.

Note: I still wonder if bootstrap is valid for G-estimation ? The marginal effect blog let me think that it is the case. It compares the delta method to an example of Pearl using bootstrap and conclude that the results are close but not identical. However, there is no reference for a proof. A good mathematical exploration of this question in the randomized case is given by Imbens and Menzel. 2018. Causal boostrap. It concludes that the bootstrap is conservative.