TMLE (Targeted Maximum Likelihood Estimation)

Definition

A procedure that corrects (targets) a plug-in estimator toward the target parameter:

1. Obtain initial estimates of the outcome regression $\bar Q^0$ and the propensity $g$ (any ML method);
2. Fluctuate $\bar Q$ (fitting $\varepsilon$) along a parametric submodel that uses the clever covariate $H(A,X)$ derived from the EIF;
3. Plug the updated $\bar Q^*$ into the target parameter. The targeting step forces the empirical EIF equation $P_n\phi(\bar Q^*,g)=0$ to be solved, yielding asymptotic efficiency + double robustness + parameter-range preservation (plug-in).

Intuitive Understanding

“Predict first, then nudge only slightly in the causal-target direction” to remove residual bias along the EIF direction. It attains the same efficiency as the One-step Estimator/AIPW, but being a plug-in it respects boundaries (e.g., probabilities).

Related Concepts

• Efficient Influence Function · One-step Estimator · AIPW · Double Machine Learning · Cross-fitting

Key Papers

• van der Laan & Rose, Targeted Learning, Springer 2011 — TMLE canonical
• Kennedy review, arXiv:2203.06469, 2022 (unifying EIF · DR · TMLE/DML)