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Bayesian Bootstrap of the Quantile Regression Estimator: A Large Sample Study

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  • Hahn, Jinyong

Abstract

The large sample property of the Bayesian bootstrap distribution of the quantile regression estimator is investigated. When the pair of dependent and independent variables are resampled, the Bayesian bootstrap is shown to converge weakly in probability to the limiting distribution of the quantile regression estimator. The Bayesian bootstrap thus has the same asymptotic distribution as the Frequentist bootstrap. In addition, the median of the Bayesian bootstrap distribution has the same asymptotic distribution as the quantile regression estimator. Copyright 1997 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • Hahn, Jinyong, 1997. "Bayesian Bootstrap of the Quantile Regression Estimator: A Large Sample Study," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 795-808, November.
    • Handle: RePEc:ier:iecrev:v:38:y:1997:i:4:p:795-808
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    Cited by:

    1. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    2. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    3. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    4. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    5. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    6. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers CWP77/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. David M. Kaplan & Lonnie Hofmann, 2019. "High-order coverage of smoothed Bayesian bootstrap intervals for population quantiles," Working Papers 1914, Department of Economics, University of Missouri, revised 19 Sep 2020.
    8. Kaplan, David M. & Zhuo, Longhao, 2021. "Frequentist properties of Bayesian inequality tests," Journal of Econometrics, Elsevier, vol. 221(1), pages 312-336.
    9. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    10. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly, 2022. "Fast algorithms for the quantile regression process," Empirical Economics, Springer, vol. 62(1), pages 7-33, January.
    11. David M. Kaplan & Longhao Zhuo, 2015. "Bayesian and frequentist inequality tests," Working Papers 1516, Department of Economics, University of Missouri, revised Feb 2018.
    12. Giuseppe Ragusa, 2007. "Bayesian Likelihoods for Moment Condition Models," Working Papers 060714, University of California-Irvine, Department of Economics.
    13. Yang Yang & Tae-Hwy Lee, 2004. "Bagging Binary Predictors for Time Series," Econometric Society 2004 Far Eastern Meetings 512, Econometric Society.
    14. Ying-Ying Lee, 2015. "Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification," Econometrics, MDPI, vol. 4(1), pages 1-14, December.
    15. Kilian, Lutz & Inoue, Atsushi & Guerron-Quintana, Pablo A., 2009. "Frequentist Inference in Weakly Identified DSGE Models," CEPR Discussion Papers 7447, C.E.P.R. Discussion Papers.

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