Finite-sample evaluation of doubly robust and deep neural network methods for causal effect estimation in nonlinear high-dimensional models

Accurate treatment effect estimation in observational studies is challenging when treatment assignment is variable and covariate overlap is limited. This study provides a finite-sample comparison of inverse probability weighting (IPW), doubly robust (DR), and neural network estimators for average treatment effect estimation. Using the Adult dataset, we compare Horvitz–Thompson and Hájek IPW estimators, a doubly robust logistic regression estimator, and neural network models with and without regularization. Performance is evaluated over 100 bootstrap replications using bias, RMSE, and sampling variability. The results show that IPW estimators can exhibit substantial bias and elevated RMSE, whereas the doubly robust estimator achieves near-zero bias and strong overall accuracy. Neural network estimators provide comparable performance, with regularization improving finite-sample stability. Overall, DR methods provide a reliable baseline, while neural networks are most useful when complex nonlinear relationships require greater flexibility and sufficient sample size is available.