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Non-crossing convex quantile regression

Author

Listed:
  • Dai, Sheng
  • Kuosmanen, Timo
  • Zhou, Xun

Abstract

Quantile crossing is a common phenomenon in shape constrained nonparametric quantile regression. A direct approach to address this problem is to impose non-crossing constraints to convex quantile regression. However, the non-crossing constraints may violate an intrinsic quantile property. This paper proposes a penalized convex quantile regression approach that can circumvent quantile crossing while maintaining the quantile property. A Monte Carlo study demonstrates the superiority of the proposed penalized approach in addressing the quantile crossing problem.

Suggested Citation

  • Dai, Sheng & Kuosmanen, Timo & Zhou, Xun, 2023. "Non-crossing convex quantile regression," Economics Letters, Elsevier, vol. 233(C).
    • Handle: RePEc:eee:ecolet:v:233:y:2023:i:c:s0165176523004226
    DOI: 10.1016/j.econlet.2023.111396
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    References listed on IDEAS

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    1. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
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    3. Tsionas, Mike G. & Assaf, A. George & Andrikopoulos, Athanasios, 2020. "Quantile stochastic frontier models with endogeneity," Economics Letters, Elsevier, vol. 188(C).
    4. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    5. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    6. Wang, Yongqiao & Wang, Shouyang & Dang, Chuangyin & Ge, Wenxiu, 2014. "Nonparametric quantile frontier estimation under shape restriction," European Journal of Operational Research, Elsevier, vol. 232(3), pages 671-678.
    7. Dai, Sheng, 2023. "Variable selection in convex quantile regression: L1-norm or L0-norm regularization?," European Journal of Operational Research, Elsevier, vol. 305(1), pages 338-355.
    8. Dai, Sheng & Kuosmanen, Timo & Zhou, Xun, 2023. "Generalized quantile and expectile properties for shape constrained nonparametric estimation," European Journal of Operational Research, Elsevier, vol. 310(2), pages 914-927.
    9. Jradi, Samah & Parmeter, Christopher F. & Ruggiero, John, 2019. "Quantile estimation of the stochastic frontier model," Economics Letters, Elsevier, vol. 182(C), pages 15-18.
    10. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    11. Zhao, Shirong, 2021. "Quantile estimation of stochastic frontier models with the normal–half normal specification: A cumulative distribution function approach," Economics Letters, Elsevier, vol. 206(C).
    12. Kuosmanen, Timo & Zhou, Xun, 2021. "Shadow prices and marginal abatement costs: Convex quantile regression approach," European Journal of Operational Research, Elsevier, vol. 289(2), pages 666-675.
    13. Holger Dette & Stanislav Volgushev, 2008. "Non‐crossing non‐parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627, July.
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    Cited by:

    1. Timo Kuosmanen & Sheng Dai, 2023. "Modeling economies of scope in joint production: Convex regression of input distance function," Papers 2311.11637, arXiv.org.
    2. Kuosmanen, Natalia & Kuosmanen, Timo & Maczulskij, Terhi & Zhou, Xun, 2024. "Least-cost Decarbonization Pathways for Electricity Generation in Finland: A Convex Quantile Regression Approach," ETLA Working Papers 114, The Research Institute of the Finnish Economy.

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