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A note on improving the efficiency of inverse probability weighted estimator using the augmentation term

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  • Han, Peisong

Abstract

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.

Suggested Citation

  • Han, Peisong, 2012. "A note on improving the efficiency of inverse probability weighted estimator using the augmentation term," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2221-2228.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2221-2228
    DOI: 10.1016/j.spl.2012.08.005
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    References listed on IDEAS

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    1. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
    2. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    3. 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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    5. Tan Zhiqiang, 2008. "Comment: Improved Local Efficiency and Double Robustness," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-9, June.
    6. Qin, Jing & Zhang, Biao & Leung, Denis H. Y., 2009. "Empirical Likelihood in Missing Data Problems," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1492-1503.
    7. Wang, Lu & Rotnitzky, Andrea & Lin, Xihong, 2010. "Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1135-1146.
    8. 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.
    9. Song Xi Chen & Denis H. Y. Leung & Jing Qin, 2008. "Improving semiparametric estimation by using surrogate data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 803-823.
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