Efficient Targeted Maximum Likelihood Estimation of Average Treatment Effects under Structured Outcome Models with Unknown Error Distributions

We study targeted maximum likelihood estimation (TMLE) of the average treatment effect in a semiparametric regression model whose mean function is indexed by a finite-dimensional parameter, while the additive error distribution is left unspecified apart from mild regularity conditions and independence from treatment and baseline covariates. The paper addresses a genuinely new causal problem: because the target depends on both the regression parameter and the unrestricted marginal law of the covariates, the regression-efficient score must be converted into a causal efficient influence function, semiparametric efficiency bound, and targeting step for the average treatment effect itself. We derive those objects, construct a cross-fitted TMLE, and establish asymptotic linearity and efficiency. In simulations, the proposed estimator is most effective when the mean is correctly structured but the error law is heavy-tailed or skewed. In these settings, it yields smaller root mean squared error and shorter intervals than Gaussian working-model inference, a standard augmented inverse-probability-weighted estimator, Bayesian additive regression trees, and a forest-based TMLE benchmark. Misspecification experiments are included to clarify the scope of the method rather than to claim universal superiority under broad mean-model failure.