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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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    1. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
    2. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-274, May-June.
    3. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    6. Bassett, Gilbert W. & Koenker, Roger W., 1992. "A note on recent proposals for computing l1 estimates," Computational Statistics & Data Analysis, Elsevier, vol. 14(2), pages 207-211, August.
    7. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(5), pages 793-813, December.
    8. Peng, Liang & Yao, Qiwei, 2003. "Least absolute deviations estimation for ARCH and GARCH models," LSE Research Online Documents on Economics 5828, London School of Economics and Political Science, LSE Library.
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. Jiancheng Jiang & Xuejun Jiang & Xinyuan Song, 2014. "Weighted composite quantile regression estimation of DTARCH models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 1-23, February.
    11. Cheng Yong Tang & Chenlei Leng, 2011. "Empirical likelihood and quantile regression in longitudinal data analysis," Biometrika, Biometrika Trust, vol. 98(4), pages 1001-1006.
    12. Yer Van Hui & Jiancheng Jiang, 2005. "Robust modelling of DTARCH models," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 143-158, July.
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    Cited by:

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    3. Zhen Yu & Keming Yu & Wolfgang K. Härdle & Xueliang Zhang & Kai Wang & Maozai Tian, 2022. "Bayesian spatio‐temporal modeling for the inpatient hospital costs of alcohol‐related disorders," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 644-667, December.
    4. 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.
    5. Sungchul Hong & Jong-June Jeon, 2023. "Uniform Pessimistic Risk and its Optimal Portfolio," Papers 2303.07158, arXiv.org, revised May 2024.
    6. Sottile, Gianluca & Frumento, Paolo, 2022. "Robust estimation and regression with parametric quantile functions," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
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    8. 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.
    9. 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.
    10. Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    11. Rong Jiang & Wei-wei Chen & Xin Liu, 2021. "Adaptive quantile regressions for massive datasets," Statistical Papers, Springer, vol. 62(4), pages 1981-1995, August.
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