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Global Bahadur representation for nonparametric censored regression quantiles and its applications

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  • Efang Kong
  • Oliver Linton

    ()
    (Institute for Fiscal Studies and Cambridge University)

  • Yingcun Xia

Abstract

This paper is concerned with the nonparametric estimation of regression quantiles where the response variable is randomly censored. Using results on the strong uniform convergence of U-processes, we derive a global Bahadur representation for the weighted local polynomial estimators, which is sufficiently accurate for many further theoretical analyses including inference. We consider two applications in detail: estimation of the average derivative, and estimation of the component functions in additive quantile regression models.

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File URL: http://cemmap.ifs.org.uk/wps/cwp3311.pdf
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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP33/11.

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Date of creation: Nov 2011
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Handle: RePEc:ifs:cemmap:33/11

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  1. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers 70, Bell Communications - Economic Research Group.
  2. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1529-1564, October.
  3. Linton, Oliver, 2001. "ESTIMATING ADDITIVE NONPARAMETRIC MODELS BY PARTIAL Lq NORM: THE CURSE OF FRACTIONALITY," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1037-1050, December.
  4. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val, 2011. "Conditional quantile processes based on series or many regressors," CeMMAP working papers CWP19/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Yannis Bilias & Roger Koenker, 2001. "Quantile regression for duration data: A reappraisal of the Pennsylvania Reemployment Bonus Experiments," Empirical Economics, Springer, vol. 26(1), pages 199-220.
  6. Arthur Lewbel & Oliver Linton, 2000. "Nonparametric Censored and Truncated Regression," Boston College Working Papers in Economics 439, Boston College Department of Economics.
  7. De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
  8. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  9. de Uña Álvarez, Jacobo & Roca Pardiñas, Javier, 2009. "Additive models in censored regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3490-3501, July.
  10. O. B. LINTON & Wolfgang HÄRDLE, 1995. "Estimation of Additive Regression Models with Links," SFB 373 Discussion Papers 1995,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  11. Chaudhuri, Probal, 1991. "Global nonparametric estimation of conditional quantile functions and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 246-269, November.
  12. Wang, Huixia Judy & Wang, Lan, 2009. "Locally Weighted Censored Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1117-1128.
  13. Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
  14. Arcones, Miguel A., 1995. "A Bernstein-type inequality for U-statistics and U-processes," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 239-247, February.
  15. Keming Yu & Zudi Lu, 2004. "Local Linear Additive Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 31(3), pages 333-346.
  16. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
  17. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  18. Honore, Bo & Khan, Shakeeb & Powell, James L., 2002. "Quantile regression under random censoring," Journal of Econometrics, Elsevier, vol. 109(1), pages 67-105, July.
  19. Guerre, Emmanuel & Sabbah, Camille, 2012. "Uniform Bias Study And Bahadur Representation For Local Polynomial Estimators Of The Conditional Quantile Function," Econometric Theory, Cambridge University Press, vol. 28(01), pages 87-129, February.
  20. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
  21. Songnian Chen & Gordon B. Dahl & Shakeeb Khan, 2005. "Nonparametric Identification and Estimation of a Censored Location-Scale Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 212-221, March.
  22. Spierdijk, Laura, 2008. "Nonparametric conditional hazard rate estimation: A local linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2419-2434, January.
  23. Lu, Xuewen & Cheng, Tsung-Lin, 2007. "Randomly censored partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1895-1922, November.
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