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Partial Linear Quantile Regression and Bootstrap Confidence Bands

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  • Wolfgang Karl Härdle
  • Ya’acov Ritov
  • Song Song

Abstract

In this paper uniform confidence bands are constructed for nonparametric quantile estimates of regression functions. The method is based on the bootstrap, where resampling is done from a suitably estimated empirical density function (edf) for residuals. It is known that the approximation error for the uniform confidence band by the asymptotic Gumbel distribution is logarithmically slow. It is proved that the bootstrap approximation provides a substantial improvement. The case of multidimensional and discrete regressor variables is dealt with using a partial linear model. Comparison to classic asymptotic uniform bands is presented through a simulation study. An economic application considers the labour market differential effect with respect to different education levels.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2010-002.

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Length: 33 pages
Date of creation: Jan 2010
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2010-002

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Keywords: Bootstrap; Quantile Regression; Confidence Bands; Nonparametric Fitting; Kernel Smoothing; Partial Linear Model;

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References

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  1. Alexandre Belloni & Victor Chernozhukov, 2009. "L1-Penalized quantile regression in high-dimensional sparse models," CeMMAP working papers CWP10/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, April.
  3. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
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  7. Efang Kong & Oliver Linton & Yingcun Xia, 2009. "Uniform Bahadur Representation for LocalPolynomial Estimates of M-Regressionand Its Application to The Additive Model," STICERD - Econometrics Paper Series /2009/535, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  9. Joel L. Horowitz, 1996. "Bootstrap Methods for Median Regression Models," Econometrics 9608004, EconWPA.
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  14. Robinson, P M, 1988. "Semiparametric Econometrics: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(1), pages 35-51, January.
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Cited by:
  1. Mengmeng Guo & Wolfgang Härdle, 2012. "Simultaneous confidence bands for expectile functions," AStA Advances in Statistical Analysis, Springer, vol. 96(4), pages 517-541, October.

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