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Robust and efficient estimation with weighted composite quantile regression

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  • Jiang, Xuejun
  • Li, Jingzhi
  • Xia, Tian
  • Yan, Wanfeng

Abstract

In this paper we introduce a weighted composite quantile regression (CQR) estimation approach and study its application in nonlinear models such as exponential models and ARCH-type models. The weighted CQR is augmented by using a data-driven weighting scheme. With the error distribution unspecified, the proposed estimators share robustness from quantile regression and achieve nearly the same efficiency as the oracle maximum likelihood estimator (MLE) for a variety of error distributions including the normal, mixed-normal, Student’s t, Cauchy distributions, etc. We also suggest an algorithm for the fast implementation of the proposed methodology. Simulations are carried out to compare the performance of different estimators, and the proposed approach is used to analyze the daily S&P 500 Composite index, which verifies the effectiveness and efficiency of our theoretical results.

Suggested Citation

  • Jiang, Xuejun & Li, Jingzhi & Xia, Tian & Yan, Wanfeng, 2016. "Robust and efficient estimation with weighted composite quantile regression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 413-423.
    • Handle: RePEc:eee:phsmap:v:457:y:2016:i:c:p:413-423
    DOI: 10.1016/j.physa.2016.03.056
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    References listed on IDEAS

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    Cited by:

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    3. Yu-Ye Zou & Han-Ying Liang, 2020. "CLT for integrated square error of density estimators with censoring indicators missing at random," Statistical Papers, Springer, vol. 61(6), pages 2685-2714, December.
    4. Sungchul Hong & Jong-June Jeon, 2023. "Uniform Pessimistic Risk and Optimal Portfolio," Papers 2303.07158, arXiv.org.
    5. Sottile, Gianluca & Frumento, Paolo, 2022. "Robust estimation and regression with parametric quantile functions," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    6. Adriano Zanin Zambom & Gregory J. Matthews, 2021. "Sure independence screening in the presence of missing data," Statistical Papers, Springer, vol. 62(2), pages 817-845, April.
    7. Jiang, Jiancheng & Jiang, Xuejun & Li, Jingzhi & Liu, Yi & Yan, Wanfeng, 2017. "Spatial quantile estimation of multivariate threshold time series models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 772-781.
    8. Peixin Zhao & Xiaoshuang Zhou, 2018. "Robust empirical likelihood for partially linear models via weighted composite quantile regression," Computational Statistics, Springer, vol. 33(2), pages 659-674, June.
    9. Yujing Shao & Lei Wang, 2022. "Optimal subsampling for composite quantile regression model in massive data," Statistical Papers, Springer, vol. 63(4), pages 1139-1161, August.
    10. Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
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