Smoothing Quantile Regressions

Marcelo Fernandes, Emmanuel Guerre and Eduardo Horta

Journal of Business & Economic Statistics, 2021, vol. 39, issue 1, 338-357

Abstract: We propose to smooth the objective function, rather than only the indicator on the check function, in a linear quantile regression context. Not only does the resulting smoothed quantile regression estimator yield a lower mean squared error and a more accurate Bahadur–Kiefer representation than the standard estimator, but it is also asymptotically differentiable. We exploit the latter to propose a quantile density estimator that does not suffer from the curse of dimensionality. This means estimating the conditional density function without worrying about the dimension of the covariate vector. It also allows for two-stage efficient quantile regression estimation. Our asymptotic theory holds uniformly with respect to the bandwidth and quantile level. Finally, we propose a rule of thumb for choosing the smoothing bandwidth that should approximate well the optimal bandwidth. Simulations confirm that our smoothed quantile regression estimator indeed performs very well in finite samples. Supplementary materials for this article are available online.

Date: 2021
References: Add references at CitEc
Citations: View citations in EconPapers (17)

Downloads: (external link)
http://hdl.handle.net/10.1080/07350015.2019.1660177 (text/html)
Access to full text is restricted to subscribers.

Related works:
Working Paper: Smoothing quantile regressions (2019)
Working Paper: Smoothing quantile regressions (2017)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:39:y:2021:i:1:p:338-357

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UBES20

DOI: 10.1080/07350015.2019.1660177

Access Statistics for this article

Journal of Business & Economic Statistics is currently edited by Eric Sampson, Rong Chen and Shakeeb Khan

More articles in Journal of Business & Economic Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().