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

TL;DR

This paper develops a new targeted maximum likelihood estimator for average treatment effects that remains efficient under unknown and potentially heavy-tailed error distributions, improving accuracy in complex models.

Contribution

It introduces a novel causal inference approach that converts regression-efficient scores into influence functions for the treatment effect, accommodating unknown error distributions.

Findings

Estimator performs well with heavy-tailed or skewed errors.

Outperforms Gaussian models, AIPW, and machine learning benchmarks in simulations.

Provides asymptotic linearity and efficiency guarantees.

Abstract

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.