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Empirical likelihood calibration estimation for the median treatment difference in observational studies

  • Wang, Qihua
  • Lai, Peng
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    The estimation of average (or mean) treatment effects is one of the most popular methods in the statistical literature. If one can have observations directly from treatment and control groups, then the simple t-statistic can be used if the underlying distributions are close to normal distributions. On the other hand, if the underlying distributions are skewed, then the median difference or the Wilcoxon statistic is preferable. In observational studies, however, each individual's choice of treatment is not completely at random. It may depend on the baseline covariates. In order to find an unbiased estimation, one has to adjust the choice probability function or the propensity score function. In this paper, we study the median treatment effect. The empirical likelihood method is used to calibrate baseline covariate information effectively. An economic dataset is used for illustration.

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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 4 (April)
    Pages: 1596-1609

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1596-1609
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    1. Changbao Wu, 2003. "Optimal calibration estimators in survey sampling," Biometrika, Biometrika Trust, vol. 90(4), pages 937-951, December.
    2. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    3. Sergio Firpo, 2004. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometric Society 2004 North American Summer Meetings 605, Econometric Society.
    4. Qin, Jing & Shao, Jun & Zhang, Biao, 2008. "Efficient and Doubly Robust Imputation for Covariate-Dependent Missing Responses," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 797-810, June.
    5. Stute, Winfried & Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood Inference in Nonlinear Errors-in-Covariables Models With Validation Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 332-346, March.
    6. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-20, September.
    7. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    8. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
    9. Huang, Chiung-Yu & Qin, Jing & Follmann, Dean A, 2008. "Empirical Likelihood-Based Estimation of the Treatment Effect in a Pretest–Posttest Study," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1270-1280.
    10. Jing Qin & Biao Zhang, 2007. "Empirical-likelihood-based inference in missing response problems and its application in observational studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 101-122.
    11. Alberto Abadie & David Drukker & Jane Leber Herr & Guido W. Imbens, 2004. "Implementing matching estimators for average treatment effects in Stata," Stata Journal, StataCorp LP, vol. 4(3), pages 290-311, September.
    12. Hua Liang & Suojin Wang & Raymond J. Carroll, 2007. "Partially linear models with missing response variables and error-prone covariates," Biometrika, Biometrika Trust, vol. 94(1), pages 185-198.
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