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Statistical consistency of coefficient-based conditional quantile regression

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  • Cai, Jia
  • Xiang, Dao-Hong

Abstract

This study focuses on the coefficient-based conditional quantile regression associated with lq-regularization term, where 1≤q≤2. Error analysis is investigated based on the capacity of the hypothesis space. The linear piecewise nature of the pinball loss function for quantile regression and the lq-penalty of the learning algorithm lead to some difficulties in the theoretical analysis. In order to overcome the difficulties, we introduce a novel error decomposition formula. The prolix iteration is then circumvented in the error analysis. Some satisfactory learning rates are achieved in a general setting under mild conditions.

Suggested Citation

  • Cai, Jia & Xiang, Dao-Hong, 2016. "Statistical consistency of coefficient-based conditional quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 1-12.
    • Handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:1-12
    DOI: 10.1016/j.jmva.2016.03.006
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    References listed on IDEAS

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    1. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
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    3. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    4. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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