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

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  • Wang, Qihua
  • Lai, Peng
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    Abstract

    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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    Bibliographic Info

    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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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Calibration Casual inference Empirical likelihood Median treatment effect Missing data Selection bias;

    References

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    1. 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.
    2. Guido W. Imbens, 2003. "Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review," NBER Technical Working Papers 0294, National Bureau of Economic Research, Inc.
    3. 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.
    4. 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.
    5. Changbao Wu, 2003. "Optimal calibration estimators in survey sampling," Biometrika, Biometrika Trust, vol. 90(4), pages 937-951, December.
    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. 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.
    8. 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.
    9. Sergio Firpo, 2004. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometric Society 2004 North American Summer Meetings 605, Econometric Society.
    10. 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.
    11. 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.
    12. 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.
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    Cited by:
    1. Arpino, Bruno & Mealli, Fabrizia, 2008. "The specification of the propensity score in multilevel observational studies," MPRA Paper 17407, University Library of Munich, Germany.
    2. Jiang, Shan & Tu, Dongsheng, 2012. "Inference on the probability P(T1," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1069-1078.

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