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Smoothing quantile regressions

Marcelo Fernandes, Emmanuel Guerre, Eduardo Horta

arXiv 21 May 2019 · Econometrics · publishedJournal of Business and Economic Statistics (2019) · 111 citations (OpenAlex)

arXiv:1905.08535 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We propose to smooth the entire objective function, rather than only 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.

Citation extraction

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
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2Newey and Powell (1990) Efficient estimation of linear and type i censored regression models under conditional quantile restrictions, Econometric Theory…1.00073100%
3Kaplan and Sun (2017) Smoothed estimating equations for instrumental variables quantile regression, Econometric Theory 33(1), 105–1571.00064100%
4Zhao (2001) Asymptotically efficient median regression in the presence of heteroskedasticity of unknown form, Econometric Theory 17(4), 765–…1.00053100%
5Koenker and Bassett (1978) Regression quantiles, Econometrica 46(1), 33–501.00053100%
6Otsu (2008) Conditional empirical likelihood estimation and inference for quantile regression models, Journal of Econometrics 142(1), 508–5380.92843100%
7Koenker (2005) Quantile Regression, Cambridge University Press0.87452100%
8Komunjer and Vuong (2010) Efficient estimation in dynamic conditional quantile models, Journal of Econometrics 157(2), 272–2850.84333100%
9Silverman (1986) Density Estimation for Statistics and Data Analysis, CRC/Chapman and Hall0.84333100%
10Portnoy (2012) Nearly root-n approximation for regression quantile processes, Annals of Statistics 40(3), 1714–17360.81142100%

Showing the top 10 of 58 scored citations.

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22412.057360.976146
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6Sparse Quantile Regression0.40511
7Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models0.40511
82309.163480.40511
9Smoothed instrumental variables quantile regression0.40511
10Ranking probabilistic forecasting models with different loss functions0.40511