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Quantile regression without the curse of unsmoothness


  • Wang, You-Gan
  • Shao, Quanxi
  • Zhu, Min


We consider quantile regression models and investigate the induced smoothing method for obtaining the covariance matrix of the regression parameter estimates. We show that the difference between the smoothed and unsmoothed estimating functions in quantile regression is negligible. The detailed and simple computational algorithms for calculating the asymptotic covariance are provided. Intensive simulation studies indicate that the proposed method performs very well. We also illustrate the algorithm by analyzing the rainfall-runoff data from Murray Upland, Australia.

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  • Wang, You-Gan & Shao, Quanxi & Zhu, Min, 2009. "Quantile regression without the curse of unsmoothness," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3696-3705, August.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:10:p:3696-3705

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    References listed on IDEAS

    1. He X. & Hu F., 2002. "Markov Chain Marginal Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 783-795, September.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, April.
    5. Yvonne H. S. Ho & Stephen M. S. Lee, 2005. "Calibrated interpolated confidence intervals for population quantiles," Biometrika, Biometrika Trust, vol. 92(1), pages 234-241, March.
    6. B. M. Brown & You-Gan Wang, 2005. "Standard errors and covariance matrices for smoothed rank estimators," Biometrika, Biometrika Trust, vol. 92(1), pages 149-158, March.
    7. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    Cited by:

    1. Fernández-Ponce, J.M. & Pellerey, F. & Rodríguez-Griñolo, M.R., 2011. "On a new NBUE property in multivariate sense: An application," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3283-3294, December.
    2. Hong, Han & Mahajan, Aprajit & Nekipelov, Denis, 2015. "Extremum estimation and numerical derivatives," Journal of Econometrics, Elsevier, vol. 188(1), pages 250-263.
    3. Thompson, Paul & Cai, Yuzhi & Moyeed, Rana & Reeve, Dominic & Stander, Julian, 2010. "Bayesian nonparametric quantile regression using splines," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1138-1150, April.
    4. Ruosha Li & Xuelin Huang & Jorge Cortes, 2016. "Quantile residual life regression with longitudinal biomarker measurements for dynamic prediction," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 755-773, November.
    5. Zhu, Min, 2013. "Return distribution predictability and its implications for portfolio selection," International Review of Economics & Finance, Elsevier, vol. 27(C), pages 209-223.
    6. Wang, You-Gan & Fu, Liya, 2011. "Rank regression for accelerated failure time model with clustered and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2334-2343, July.
    7. Pang, Lei & Lu, Wenbin & Wang, Huixia Judy, 2012. "Variance estimation in censored quantile regression via induced smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 785-796.
    8. Fu, Liya & Wang, You-Gan & Bai, Zhidong, 2010. "Rank regression for analysis of clustered data: A natural induced smoothing approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1036-1050, April.
    9. Fu, Liya & Wang, You-Gan, 2012. "Quantile regression for longitudinal data with a working correlation model," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2526-2538.
    10. Shuanghua Luo & Changlin Mei & Cheng-yi Zhang, 2017. "Smoothed empirical likelihood for quantile regression models with response data missing at random," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 95-116, January.

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