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The kth power expectile regression

Author

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  • Yingying Jiang

    (Sichuan University of Science and Engineering
    Southwestern University of Finance and Economics)

  • Fuming Lin

    (Sichuan University of Science and Engineering
    Shanghai University of Finance and Economics)

  • Yong Zhou

    (East China Normal University
    Chinese Academy of Sciences)

Abstract

Check functions of least absolute deviation make sure quantile regression methods are robust, while squared check functions make expectiles more sensitive to the tails of distributions and more effective for the normal case than quantiles. In order to balance robustness and effectiveness, we adopt a loss function, which falls in between the above two loss functions, to introduce a new kind of expectiles and develop an asymmetric least kth power estimation method that we call the kth power expectile regression, k larger than 1 and not larger than 2. The asymptotic properties of the corresponding estimators are provided. Simulation results show that the asymptotic efficiency of the kth power expectile regression is higher than those of the common quantile regression and expectile regression in some data cases. A primary procedure of choosing satisfactory k is presented. We finally apply our method to the real data.

Suggested Citation

  • Yingying Jiang & Fuming Lin & Yong Zhou, 2021. "The kth power expectile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 83-113, February.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-019-00738-y
    DOI: 10.1007/s10463-019-00738-y
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    References listed on IDEAS

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