Partial Linear Quantile Regression and Bootstrap Confidence Bands

SFB 649 Discussion Paper 2010-002

33 Pages Posted: 9 Jan 2017

See all articles by Wolfgang Karl Härdle

Wolfgang Karl Härdle

Blockchain Research Center Humboldt-Universität zu Berlin; Charles University; National Yang Ming Chiao Tung University; Asian Competitiveness Institute

Ya'acov Ritov

Hebrew University of Jerusalem

Song Song

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Date Written: November 28, 2009

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

JEL Classification: C14, C21, C31, J01, J31, J71

Suggested Citation

Härdle, Wolfgang Karl and Ritov, Ya'acov and Song, Song, Partial Linear Quantile Regression and Bootstrap Confidence Bands (November 28, 2009). SFB 649 Discussion Paper 2010-002, Available at SSRN: https://ssrn.com/abstract=2894242 or http://dx.doi.org/10.2139/ssrn.2894242

Wolfgang Karl Härdle (Contact Author)

Blockchain Research Center Humboldt-Universität zu Berlin ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

Asian Competitiveness Institute ( email )

Singapore

Ya'acov Ritov

Hebrew University of Jerusalem ( email )

Mount Scopus
Jerusalem, Jerusalem 91905
Israel

Song Song

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Spandauer Strasse 1
Berlin, D-10178
Germany

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