From Conditional Quantile Regression to Marginal Quantile Estimation with Applications to Missing Data and Causal Inference

References

• 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.
   Google Scholar
• Chen, X., Linton, O., and Van Keilegom,I. (2003),“Estimation of Semiparametric Models when the Criterion Function is not Smooth,” Econometrica, 71, 1591–1608. DOI: 10.1111/1468-0262.00461.
   Web of Science ®Google Scholar
• Chernozhukov, V., Fernández-Val, I., and Melly, B. (2013), “Inference on Counterfactual Distributions,” Econometrica, 81, 2205–2268.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Donald, S. G., and Hsu, Y.-C. (2014), “Estimation and Inference for Distribution Functions and Quantile Functions in Treatment Effect Models,” Journal of Econometrics, 178, 383–397. DOI: 10.1016/j.jeconom.2013.03.010.
   Web of Science ®Google Scholar
• Firpo, S. (2007), “Efficient Semiparametric Estimation of Quantile Treatment Effects,” Econometrica, 75, 259–276. DOI: 10.1111/j.1468-0262.2007.00738.x.
   Web of Science ®Google Scholar
• Gutenbrunner, C., and Jurecková, J. (1992), “Regression Quantile and Regression Rank Score Process in the Linear Model and Derived Statistics,” Annals of Statistics, 20, 305–330.
   Web of Science ®Google Scholar
• Hirano, K., Imbens, G. W., and Ridder, G. (2003), “Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score,” Econometrica, 71, 1161–1189. DOI: 10.1111/1468-0262.00442.
   Web of Science ®Google Scholar
• Imbens, G. W., and Rubin, D. B. (2015), Causal Inference in Statistics, Social, and Biomedical Sciences, Cambridge: Cambridge University Press.
   Google Scholar
• Kianian, B., Kim, J. I., Fine, J. P., and Peng, L. (2021), “Causal Proportional Hazards Estimation with a Binary Instrumental Variable,” Statistica Sinica, 31, 673–699. DOI: 10.5705/ss.202019.0096.
   PubMed Web of Science ®Google Scholar
• Koenker, R. (2005), Quantile Regression, New York: Cambridge University Press.
   Google Scholar
• Koenker, R., and Bassett, G. (1978), “Regression Quantiles,” Econometrica, 46, 33–50. DOI: 10.2307/1913643.
   Web of Science ®Google Scholar
• LaLonde, R. J. (1986), “Evaluating the Econometric Evaluations of Training Programs with Experimental Data,” The American Economic Review, 76, 604–620.
   Web of Science ®Google Scholar
• Little, R. J. A., and Rubin, D. B. (2002), Statistical Analysis with Missing Data (2nd ed.), New York: Wiley.
   Google Scholar
• Matloff, N. S. (1981), “Use of Regression Functions for Improved Estimation of Means,” Biometrika, 68, 685–689. DOI: 10.1093/biomet/68.3.685.
   Web of Science ®Google Scholar
• Peng, L., and Fine, J. (2009), “Competing Risks Quantile Regression,” Journal of the American Statistical Association, 104, 1440–1453. DOI: 10.1198/jasa.2009.tm08228.
   Web of Science ®Google Scholar
• Qin, J. (2017), Biased Sampling, Over-identified Parameter Problems and Beyond, Singapore: Springer.
   Google Scholar
• Robins, J. M., Rotnitzky, A., 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.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Rubin, D. B. (1974), “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies,” Journal of Educational Psychology, 66, 688–701. DOI: 10.1037/h0037350.
   Web of Science ®Google Scholar
• Stock, J. H. (1991), “Nonparametric ‘Policy Analysis: An Application to Estimating Hazardous Waste Cleanup Benefits,” in Nonparametric and Semiparametric Methods in Econometrics and Statistics, eds. W. Barnett, J. Powell, and G. Tauchen, pp. 77–98, Cambridge: Cambridge University Press.
   Google Scholar
• van der Vaart, A., and Wellner, J. (1996), Weak Convergence and Empirical Processes: with Application to Statistics, New York: Springer Verlag.
   Google Scholar
• Wang, H. J., Li, D., and He, X. (2012), “Estimation of High Conditional Quantiles for Heavy-Tailed Distributions,” Journal of the American Statistical Association, 107, 1453–1464. DOI: 10.1080/01621459.2012.716382.
   Web of Science ®Google Scholar
• Wang, H. J., and Zhou, X.-H. (2010),“‘Estimation of the Retransformed Conditional Mean in Health Care Cost Studies,” Biometrika, 97, 147–158. DOI: 10.1093/biomet/asp072.
   Web of Science ®Google Scholar