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Articles

Optimal Covariate Balancing Conditions in Propensity Score Estimation

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References

  • Abadie, A., and Imbens, G. W. (2006), “Large Sample Properties of Matching Estimators for Average Treatment Effects,” Econometrica, 74, 235–267. DOI: 10.1111/j.1468-0262.2006.00655.x.
  • Ai, C., Linton, O., Motegi, K., and Zhang, Z. (2021), “A Unified Framework for Efficient Estimation of General Treatment Models,” Quantitative Economics, 12, 779–816. DOI: 10.3982/QE1494.
  • Andrews, D. W. (1991), “Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models,” Econometrica, 307–345. DOI: 10.2307/2938259.
  • Arcones, M. A. (1995), “A Bernstein-Type Inequality for u-Statistics and u-Processes,” Statistics & Probability Letters, 22, 239–247.
  • Bang, H., and Robins, J. M. (2005), “Doubly Robust Estimation in Missing Data and Causal Inference Models,” Biometrics, 61, 962–973. DOI: 10.1111/j.1541-0420.2005.00377.x.
  • Benkeser, D., Carone, M., van der Laan, M. J., and Gilbert, P. B. (2017), “Doubly-Robust Nonparametric Inference on the Average Treatment Effect,” Biometrika, 104, 863–880. DOI: 10.1093/biomet/asx053.
  • Bickel, P. J., Klaassen, C. A., Ritov, Y., Wellner, J. A. (1998), Efficient and Adaptive Estimation for Semiparametric Models, Springer-Verlag.
  • Cao, W., Tsiatis, A. A., and Davidian, M. (2009), “Improving Efficiency and Robustness of the Doubly Robust Estimator for a Population Mean With Incomplete Data,” Biometrika, asp033. DOI: 10.1093/biomet/asp033.
  • Chan, K. C. G., Yam, S. C. P., and Zhang, Z. (2016), “Globally Efficient Nonparametric Inference of Average Treatment Effects by Empirical Balancing Calibration Weighting,” Journal of the Royal Statistical Society, Series B, 78, 673–700. DOI: 10.1111/rssb.12129.
  • Chen, X. (2007), “Large Sample Sieve Estimation of Semi-Nonparametric Models,” Handbook of Econometrics, 6, 5549–5632.
  • Copas, J., and Eguchi, S. (2005), “Local Model Uncertainty and Incomplete-Data Bias,” Journal of the Royal Statistical Society, 67, 459–513. DOI: 10.1111/j.1467-9868.2005.00512.x.
  • Dehejia, R. H., and Wahba, S. (1999), “Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs,” Journal of the American Statistical Association, 94, 1053–1062. DOI: 10.1080/01621459.1999.10473858.
  • Fong, C., Hazlett, C., and Imai, K. (2018a), “Covariate Balancing Propensity Score for a Continuous Treatment: Application to the Efficacy of Political Advertisements,” Annals of Applied Statistics, 12, 156–177.
  • Fong, C., Hazlett, C., and Imai, K. (2018b), “CBPS: R Package for Covariate Balancing Propensity Score.” Comprehensive R Archive Network (CRAN), available at: https://CRAN.R-project.org/package=CBPS.
  • Frölich, M., Huber, M. and Wiesenfarth, M. (2015), “The Finite Sample Performance of Semi- and Nonparametric Estimators for Treatment Effects and Policy Evaluation,” Tech. rep., IZA discussion paper No. 8756.
  • Graham, B. S., Pinto, C., and Egel, D. (2012), “Inverse Probability Tilting for Moment Condition Models With Missing Data,” Review of Economic Studies, 79, 1053–1079. DOI: 10.1093/restud/rdr047.
  • Hahn, J. (1998), “On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects,” Econometrica, 66, 315–331. DOI: 10.2307/2998560.
  • Hainmueller, J. (2012), “Entropy Balancing for Causal Effects: Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies,” Political Analysis, 20, 25–46. DOI: 10.1093/pan/mpr025.
  • Han, P., and Wang, L. (2013), “Estimation With Missing Data: Beyond Double Robustness,” Biometrika, ass087. DOI: 10.1093/biomet/ass087.
  • Hansen, L. P. (1982), “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, 50, 1029–1054. DOI: 10.2307/1912775.
  • Henmi, M., and Eguchi, S. (2004), “A Paradox Concerning Nuisance Parameters and Projected Estimating Functions,” Biometrika, 91, 929–941. DOI: 10.1093/biomet/91.4.929.
  • Hirano, K., Imbens, G., and Ridder, G. (2003), “Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score,” Econometrica, 71, 1307–1338.
  • Horvitz, D., and Thompson, D. (1952), “A Generalization of Sampling Without Replacement From a Finite Universe,” Journal of the American Statistical Association, 47, 663–685. DOI: 10.1080/01621459.1952.10483446.
  • Imai, K., and Ratkovic, M. (2014), “Covariate Balancing Propensity Score,” Journal of the Royal Statistical Society, 76, 243–263. DOI: 10.1111/rssb.12027.
  • Imai, K., and Ratkovic, M. (2015), “Robust Estimation of Inverse Probability Weights for Marginal Structural Models,” Journal of the American Statistical Association, 110, 1013–1023.
  • Imbens, G. W., Newey, W. K., and Ridder, G. (2007), “Mean-Square-Error Calculations for Average Treatment Effects,” Technical Report.
  • Kang, J. D. Y., and Schafer, J. L. (2007), “Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean From Incomplete Data,” Statistical Science, 22, 574–580.
  • LaLonde, R. J. (1986), “Evaluating the Econometric Evaluations of Training Programs With Experimental Data,” The American Economic Review, 76, 604–620.
  • Newey, W. K. (1997), “Convergence Rates and Asymptotic Normality for Series Estimators,” Journal of Econometrics, 79, 147–168. DOI: 10.1016/S0304-4076(97)00011-0.
  • Newey, W. K., and McFadden, D. (1994), “Large Sample Estimation and Hypothesis Testing,” Handbook of Econometrics, 4, 2111–2245.
  • Ning, Y., Peng, S., and Imai, K. (2018), “Robust Estimation of Causal Effects Via High-Dimensional Covariate Balancing Propensity Score.” arXiv:1812.08683 .
  • Owen, A. B. (2001), Empirical Likelihood, New York: Chapman & Hall/CRC.
  • Qin, J., and Zhang, B. (2007), “Empirical-Likelihood-Based Inference in Missing Response Problems and Its Application in Observational Studies,” Journal of the Royal Statistical Society, 69, 101–122.
  • Robins, J., Sued, M., Lei-Gomez, Q., and Rotnitzky, A. (2007), “Comment: Performance of Double-Robust Estimators When Inverse Probability Weights Are Highly Variable,” Statistical Science, 22, 544–559. DOI: 10.1214/07-STS227D.
  • Robins, J. M., Rotnitzky, A., and Zhao, L. P. (1994), “Estimation of Regression Coefficients When Some Regressors Are Not Always Observed,” Journal of the American Statistical Association, 89, 846–866. DOI: 10.1080/01621459.1994.10476818.
  • Robins, J. M., Rotnitzky, A., and Zhao, L. P. (1995), “Analysis of Semiparametric Regression Models for Repeated Outcomes in the Presence of Missing Data,” Journal of the American Statistical Association 90 106–121. DOI: 10.1080/01621459.1995.10476493.
  • Rosenbaum, P. R., and Rubin, D. B. (1983), “The Central Role of the Propensity Score in Observational Studies for Causal Effects,” Biometrika, 70, 41–55. DOI: 10.1093/biomet/70.1.41.
  • Rotnitzky, A., Lei, Q., Sued, M., and Robins, J. M. (2012). “Improved Double-Robust Estimation in Missing Data and Causal Inference Models,” Biometrika, 99, 439–456. DOI: 10.1093/biomet/ass013.
  • Rubin, D. B. (1990), “Comments on ‘On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9’ by J. Splawa-Neyman Translated from the Polish and edited by D. M. Dabrowska and T. P. Speed,” Statistical Science. 472–480.
  • Smith, J. A., and Todd, P. E. (2005), “Does Matching Overcome Lalonde’s Critique of Nonexperimental Estimators?” Journal of Econometrics, 125, 305–353.
  • Tan, Z. (2006), “A Distributional Approach for Causal Inference Using Propensity Scores,” Journal of the American Statistical Association, 101, 1619–1637. DOI: 10.1198/016214506000000023.
  • Tan, Z. (2010), “Bounded, Efficient and Doubly Robust Estimation With Inverse Weighting,” Biometrika, 97, 661–682.
  • Tropp, J. A. (2015), “An Introduction to Matrix Concentration Inequalities,” arXiv:1501.01571.
  • van der Laan, M. J. (2010), “Targeted Maximum Likelihood Based Causal Inference: Part I,” The International Journal of Biostatistics, 6, 2. DOI: 10.2202/1557-4679.1211.
  • Vermeulen, K., and Vansteelandt, S. (2015), “Bias-Reduced Doubly Robust Estimation,” Journal of the American Statistical Association, 110, 1024–1036. DOI: 10.1080/01621459.2014.958155.
  • Wyss, R., Ellis, A. R., Brookhart, M. A., Girman, C. J., Funk, M. J., LoCasale, R., and Stürmer, T. (2014), “The Role of Prediction Modeling in Propensity Score Estimation: An Evaluation of Logistic Regression, bCART, and the Covariate-Balancing Propensity Score,” American Journal of Epidemiology 180, 645–655. DOI: 10.1093/aje/kwu181.
  • Zhao, Q. (2019), “Covariate Balancing Propensity Score by Tailored Loss Functions,” The Annals of Statistics, 47, 965–993. DOI: 10.1214/18-AOS1698.
  • Zhao, Q., and Percival, D. (2017), “Primal–Dual Covariate Balance and Minimal Double Robustness Via Entropy Balancing,” Journal of Causal Inference, 5.
  • Zubizarreta, J. R. (2015), “Stable Weights That Balance Covariates for Estimation With Incomplete Outcome Data,” Journal of the American Statistical Association, 110, 910–922. DOI: 10.1080/01621459.2015.1023805.

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