Constructing targeted minimum loss/maximum likelihood estimators: a simple illustration to build intuition

Machine learning is increasingly used to estimate nuisance functions in causal inference. The efficient influence function (EIF) offers a principled way to construct estimators that can incorporate machine learning with valid inference (eg, estimate valid conference intervals). In this tutorial, we illustrate how to construct targeted maximum likelihood/minimum loss estimators from the EIF, a topic that is well covered in statistical literature but remains less accessible to applied researchers. A companion paper, Renson et al. 2025 (AJE, kwaf169) provides a thorough, but approachable description of the EIF and its derivation for a statistical estimand.