Partial linear quantile regression and bootstrap confidence bands

Wolfgang Härdle, Ya'acov Ritov and Song Song

No 2010-002, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

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.

Keywords: Bootstrap; Quantile Regression; Confidence Bands; Nonparametric Fitting; Kernel Smoothing; Partial Linear Model (search for similar items in EconPapers)
JEL-codes: C14 C21 C31 J01 J31 J71 (search for similar items in EconPapers)
Date: 2010
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