A note on improving the efficiency of inverse probability weighted estimator using the augmentation term
AbstractThe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 82 (2012)
Issue (Month): 12 ()
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Tan Zhiqiang, 2008. "Comment: Improved Local Efficiency and Double Robustness," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-9, June.
- 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.
- 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.
- repec:cup:cbooks:9780521496032 is not listed on IDEAS
- Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
- 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.
- Rubin Daniel B & van der Laan Mark J., 2008. "Empirical Efficiency Maximization: Improved Locally Efficient Covariate Adjustment in Randomized Experiments and Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-40, May.
- 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.
- 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.
If references are entirely missing, you can add them using this form.