A note on improving the efficiency of inverse probability weighted estimator using the augmentation term
The augmented inverse probability weighted (AIPW) estimator employing the optimal augmentation term is more efficient than the inverse probability weighted (IPW) estimator. However, the AIPW estimator could lose substantial efficiency compared to the IPW estimator when the optimal augmentation term is incorrectly modeled. We propose a modified AIPW (MAIPW) estimator by adapting Tan’s (2010b) “tilde” estimator, which was proposed for structural models, for regression models with missing data. When the missing mechanism is correctly modeled, the proposed MAIPW estimator is more efficient than the IPW estimator, and is more efficient than the AIPW estimator using the same augmentation term, except when the augmentation term is a correct model for the optimal one, in which case both MAIPW and AIPW estimators attain the semiparametric efficiency bound, thus are equally efficient. In addition, like the AIPW estimator, the MAIPW estimator is doubly robust. Through simulation experiments, we compare numerical performances of the MAIPW estimator and some other estimators that attempt to improve efficiency upon the IPW estimator.
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Volume (Year): 82 (2012)
Issue (Month): 12 ()
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- Tan, Zhiqiang, 2006. "A Distributional Approach for Causal Inference Using Propensity Scores," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1619-1637, December.
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- Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
- Andrea Rotnitzky & Quanhong Lei & Mariela Sued & James M. Robins, 2012. "Improved double-robust estimation in missing data and causal inference models," Biometrika, Biometrika Trust, vol. 99(2), pages 439-456.
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