A Simulation Study of the Doubly Robust Estimator of Benkeser, Carone, Van Der Laan and Gilbert

Abstract

Doubly robust methods have garnered significant attention in estimating Average Treatment Effect (ATE) due to their robustness to model misspecification and adaptability to diverse datasets. However, conventional doubly robust methods often demonstrate inconsistency when one of the nuisance parameters is inconsistently estimated (Benkeser et al. (2017)). In this thesis, we delve into the performance of the six ATE estimators discussed in Benkeser et al. (2017) and identify irregularities in the proposed formulations. First, we review fundamental concepts and results regarding regularity and asymptotic linearity. Then, through a comprehensive simulation study, we explore the performance of these estimators across varying sample sizes and data-generating processes. Our simulations uncover instances where the estimators proposed by Benkeser et al. (2017) exhibit behavior significantly deviating from expectations for the coverage of confidence intervals under specific data-generating processes. Our results call for more extensive simulation studies of these estimators before recommending their widespread use, as they may lead to poor coverage confidence intervals, potentially compromising inferential conclusions' reliability.