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Smoothing quantile regressions

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  • Fernandes, Marcelo
  • Guerre, Emmanuel
  • Horta, Eduardo

Abstract

We propose to smooth the entire objective function rather than only the check function in a linear quantile regression context. We derive a uniform Bahadur-Kiefer representation for the resulting convolution-type kernel estimator that demonstrates it improves on the extant quantile regression estimators in the literature. In addition, we also show that it is straightforward to compute asymptotic standard errors for the quantile regression coefficient estimates as well as to implement Wald-type tests. Simulations confirm that our smoothed quantile regression estimator performs very well in finite samples.

Suggested Citation

  • Fernandes, Marcelo & Guerre, Emmanuel & Horta, Eduardo, 2017. "Smoothing quantile regressions," Textos para discussão 457, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    • Handle: RePEc:fgv:eesptd:457
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    Cited by:

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    2. Songnian Chen & Junlong Feng, 2025. "Universal Factor Models," Papers 2501.15761, arXiv.org, revised Jul 2025.
    3. James Mitchell & Aubrey Poon & Dan Zhu, 2024. "Constructing density forecasts from quantile regressions: Multimodality in macrofinancial dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 790-812, August.
    4. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    5. Chen, Le-Yu & Lee, Sokbae, 2023. "Sparse quantile regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 2195-2217.
    6. Kean Ming Tan & Lan Wang & Wen‐Xin Zhou, 2022. "High‐dimensional quantile regression: Convolution smoothing and concave regularization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 205-233, February.
    7. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2020. "Forecasting value at risk with intra-day return curves," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1023-1038.
    8. Abankwah, Stephen Asare & Afriyie, Samuel Osei, 2025. "Modelling Sustainable Energy Transition in BRICS+ Countries: A Smoothed Common Correlated Effects Instrumental Variable Quantile Regression Approach," MPRA Paper 123758, University Library of Munich, Germany.
    9. Zhaohan Hou & Wei Ma & Lei Wang, 2023. "Sparse and debiased lasso estimation and inference for high-dimensional composite quantile regression with distributed data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(4), pages 1230-1250, December.
    10. Maria Laura Battagliola & Helle Sørensen & Anders Tolver & Ana-Maria Staicu, 2025. "Quantile Regression for Longitudinal Functional Data with Application to Feed Intake of Lactating Sows," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 30(1), pages 211-230, March.
    11. Tae-Hwy Lee & Aman Ullah & He Wang, 2024. "The second-order bias and mean squared error of quantile regression estimators," Indian Economic Review, Springer, vol. 59(1), pages 11-68, October.
    12. Mario Forni & Luca Gambetti & Nicolò Maffei-Faccioli & Luca Sala, 2023. "The impact of financial shocks on the forecast distribution of output and inflation," Working Paper 2023/3, Norges Bank.
    13. Tomasz Serafin & Bartosz Uniejewski, 2024. "Ranking probabilistic forecasting models with different loss functions," Papers 2411.17743, arXiv.org.
    14. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    15. He, Xuming & Pan, Xiaoou & Tan, Kean Ming & Zhou, Wen-Xin, 2023. "Smoothed quantile regression with large-scale inference," Journal of Econometrics, Elsevier, vol. 232(2), pages 367-388.
    16. Rong Jiang & Siu Kai Choy & Keming Yu, 2024. "Non‐crossing quantile double‐autoregression for the analysis of streaming time series data," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(4), pages 513-532, July.
    17. Tae-Hwy Lee & Aman Ullah & He Wang, 2023. "The Second-order Bias and Mean Squared Error of Quantile Regression Estimators," Working Papers 202313, University of California at Riverside, Department of Economics.
    18. Bartosz Uniejewski, 2023. "Smoothing Quantile Regression Averaging: A new approach to probabilistic forecasting of electricity prices," Papers 2302.00411, arXiv.org, revised Nov 2024.
    19. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2023. "Smoothing the Nonsmoothness," Papers 2309.16348, arXiv.org.
    20. Venkatram Kari & Geetha Mary Amalanathan, 2025. "Targeted prevention of risky deals for improper granular data with deep learning," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 16(2), pages 750-764, February.
    21. Eduardo Schirmer Finn & Eduardo Horta, 2024. "Convolution Mode Regression," Papers 2412.05736, arXiv.org.
    22. Forni, Mario & Gambetti, Luca & Maffei-Faccioli, Nicolò & Sala, Luca, 2024. "The effects of monetary policy on macroeconomic risk," European Economic Review, Elsevier, vol. 167(C).
    23. Jean-Jacques Forneron, 2023. "Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models," Papers 2301.07196, arXiv.org, revised Feb 2023.
    24. Ufuk Beyaztas & Han Lin Shang & Semanur Saricam, 2025. "Penalized function-on-function linear quantile regression," Computational Statistics, Springer, vol. 40(1), pages 301-329, January.
    25. Grigory Franguridi & Bulat Gafarov & Kaspar Wüthrich, 2021. "Conditional Quantile Estimators: A Small Sample Theory," CESifo Working Paper Series 9046, CESifo.

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