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Quantile regression and variable selection of single-index coefficient model

Author

Listed:
  • Weihua Zhao

    (East China Normal University
    NanTong University)

  • Riquan Zhang

    (East China Normal University)

  • Yazhao Lv

    (East China Normal University)

  • Jicai Liu

    (East China Normal University
    Shanghai Normal University)

Abstract

In this paper, a minimizing average check loss estimation (MACLE) procedure is proposed for the single-index coefficient model (SICM) in the framework of quantile regression (QR). The resulting estimators have the asymptotic normality and achieve the best convergence rate. Furthermore, a variable selection method is investigated for the QRSICM by combining MACLE method with the adaptive LASSO penalty, and we also established the oracle property of the proposed variable selection method. Extensive simulations are conducted to assess the finite sample performance of the proposed estimation and variable selection procedure under various error settings. Finally, we present a real-data application of the proposed approach.

Suggested Citation

  • Weihua Zhao & Riquan Zhang & Yazhao Lv & Jicai Liu, 2017. "Quantile regression and variable selection of single-index coefficient model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 761-789, August.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:4:d:10.1007_s10463-016-0558-9
    DOI: 10.1007/s10463-016-0558-9
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    References listed on IDEAS

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    7. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
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    Cited by:

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    3. Wang, Lei & Zhang, Jing & Li, Bo & Liu, Xiaohui, 2022. "Quantile trace regression via nuclear norm regularization," Statistics & Probability Letters, Elsevier, vol. 182(C).
    4. Rong Jiang & Mengxian Sun, 2022. "Single-index composite quantile regression for ultra-high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 443-460, June.

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