• Corpus ID: 219124092

Doubly robust estimation of average treatment effect revisited

@article{Guo2020DoublyRE,
  title={Doubly robust estimation of average treatment effect revisited},
  author={Keli Guo and Chuyun Ye and Jun Fan and Li-Zhi Fang Division of Applied Mathematics and Hong Kong Baptist University and Hong Kong and Center for Statistics and Data Science and Beijing Normal University and Zhuhai and China. and School of Statistics and Beijing},
  journal={arXiv: Statistics Theory},
  year={2020}
}

• Keli Guo, C. Ye, +10 authors Beijing
• Published 29 May 2020
• Mathematics, Economics
• arXiv: Statistics Theory

The research described herewith is to re-visit the classical doubly robust estimation of average treatment effect by conducting a systematic study on the comparisons, in the sense of asymptotic efficiency, among all possible combinations of the estimated propensity score and outcome regression. To this end, we consider all nine combinations under, respectively, parametric, nonparametric and semiparametric structures. The comparisons provide useful information on when and how to efficiently utilize the model structures in practice. Further, when there is model-misspecification, either propensity score or outcome regression, we also give the corresponding comparisons. Three phenomena are observed. Firstly, when all models are correctly specified, any combination can achieve the same semiparametric efficiency bound, which coincides with the existing results of some combinations. Secondly, when the propensity score is correctly modeled and estimated, but the outcome regression is misspecified parametrically or semiparametrically, the asymptotic variance is always larger than or equal to the semiparametric efficiency bound. Thirdly, in contrast, when the propensity score is misspecified parametrically or semiparametrically, while the outcome regression is correctly modeled and estimated, the asymptotic variance is not necessarily larger than the semiparametric efficiency bound. In some cases, the "super-efficiency" phenomenon occurs. We also conduct a small numerical study.