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Single-index composite quantile regression with heteroscedasticity and general error distributions

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  • Rong Jiang
  • Wei-Min Qian
  • Zhan-Gong Zhou

Abstract

It is known that composite quantile regression (CQR) could be much more efficient and sometimes arbitrarily more efficient than the least squares estimator. Based on CQR method, we propose a weighted CQR (WCQR) method for single-index models with heteroscedasticity and general error distributions. Because of the use of weights, the estimation bias is eliminated asymptotically. By comparing asymptotic relative efficiency, WCQR estimation outperforms the CQR estimation and least squares estimation. The simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2016. "Single-index composite quantile regression with heteroscedasticity and general error distributions," Statistical Papers, Springer, vol. 57(1), pages 185-203, March.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:1:p:185-203
    DOI: 10.1007/s00362-014-0646-y
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    Cited by:

    1. Ash Abebe & Huybrechts F. Bindele & Masego Otlaadisa & Boikanyo Makubate, 2021. "Robust estimation of single index models with responses missing at random," Statistical Papers, Springer, vol. 62(5), pages 2195-2225, October.
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    3. Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    4. Qifa Xu & Chao Cai & Cuixia Jiang & Fang Sun & Xue Huang, 2020. "Block average quantile regression for massive dataset," Statistical Papers, Springer, vol. 61(1), pages 141-165, February.
    5. Jiang, Rong & Qian, Wei-Min & Zhou, Zhan-Gong, 2016. "Weighted composite quantile regression for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 34-48.
    6. Y. Andriyana & I. Gijbels & A. Verhasselt, 2018. "Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity," Statistical Papers, Springer, vol. 59(4), pages 1589-1621, December.
    7. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.
    8. Wang, Kangning & Li, Shaomin & Zhang, Benle, 2021. "Robust communication-efficient distributed composite quantile regression and variable selection for massive data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).

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