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Statistical inference for the functional quadratic quantile regression model

Author

Listed:
  • Gongming Shi

    (Beijing University of Technology)

  • Tianfa Xie

    (Beijing University of Technology
    Collaborative Innovation Center on Capital Social Construction and Social Management, Beijing University of Technology)

  • Zhongzhan Zhang

    (Beijing University of Technology
    Collaborative Innovation Center on Capital Social Construction and Social Management, Beijing University of Technology)

Abstract

In this paper, we develop statistical inference procedures for functional quadratic quantile regression model in which the response is a scalar and the predictor is a random function defined on a compact set of R. The functional coefficients are estimated by functional principal components. The asymptotic properties of the resulting estimators are established under mild conditions. In order to test the significance of the nonlinear term in the model, we propose a rank score test procedure. The asymptotic properties of the proposed test statistic are established. The proposed method provides a highly efficient and robust alternative to the least squares method, and can be conveniently implemented using existing R software package. Finally, we examine the performance of the proposed method for finite sample sizes by Monte Carlo simulation studies and illustrate it with a real data example.

Suggested Citation

  • Gongming Shi & Tianfa Xie & Zhongzhan Zhang, 2020. "Statistical inference for the functional quadratic quantile regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 937-960, November.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:8:d:10.1007_s00184-020-00763-5
    DOI: 10.1007/s00184-020-00763-5
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    References listed on IDEAS

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