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Smoothing Quantile Regressions

Fernandes, Marcelo, Guerre, Emmanuel, Horta, Eduardo (2019) Smoothing Quantile Regressions. Journal of Business and Economic Statistics, . ISSN 0735-0015. E-ISSN 1537-2707. (doi:10.1080/07350015.2019.1660177) (KAR id:76315)

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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.

Item Type: Article
DOI/Identification number: 10.1080/07350015.2019.1660177
Uncontrolled keywords: Asymptotic expansion; Bahadur–Kiefer representation; Conditional quantile; Convolution-based smoothing; Data-driven bandwidth.
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HB Economic Theory
Divisions: Divisions > Division of Human and Social Sciences > School of Economics
Depositing User: Emmanuel Guerre
Date Deposited: 10 Sep 2019 11:01 UTC
Last Modified: 16 Feb 2021 14:07 UTC
Resource URI: (The current URI for this page, for reference purposes)
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