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Partial Linear Quantile Regression and Bootstrap Confidence Bands

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

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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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2010-002.pdf
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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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