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Analysis of the positive response data with the varying coefficient partially nonlinear multiplicative model

Author

Listed:
  • Huilan Liu

    (Guizhou University)

  • Xiawei Zhang

    (Guizhou University
    Army Infantry Academy)

  • Huaiqing Hu

    (Guizhou University)

  • Junjie Ma

    (Guizhou University)

Abstract

In this paper, we propose a novel varying coefficient partially nonlinear multiplicative model (VCPNLMM) to handle positive response data in a flexible way. The unknown parameters and functions arising in the model are estimated by a local least product relative error (LLPRE) algorithm which is developed based on the technique of the local kernel smoothing. With the help of quadratic approximation lemma and Lyapunov’s central limit theorem, the convergence properties of the proposed estimators are established. A new goodness-of-fit test is proposed to check whether the coefficient functions are constants or not. Experiments and the real data analysis are conducted to illustrate the performance of the new estimators and testing procedures.

Suggested Citation

  • Huilan Liu & Xiawei Zhang & Huaiqing Hu & Junjie Ma, 2024. "Analysis of the positive response data with the varying coefficient partially nonlinear multiplicative model," Statistical Papers, Springer, vol. 65(5), pages 3063-3092, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01516-y
    DOI: 10.1007/s00362-023-01516-y
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    References listed on IDEAS

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    1. Zhouping Li & Yuanyuan Lin & Guoliang Zhou & Wang Zhou, 2014. "Empirical likelihood for least absolute relative error regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 86-99, March.
    2. Hao Ding & Zhanfeng Wang & Yaohua Wu, 2018. "A relative error-based estimation with an increasing number of parameters," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(1), pages 196-209, January.
    3. Chen, Kani & Guo, Shaojun & Lin, Yuanyuan & Ying, Zhiliang, 2010. "Least Absolute Relative Error Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1104-1112.
    4. Jun Zhang & Junpeng Zhu & Yan Zhou & Xia Cui & Tao Lu, 2020. "Multiplicative regression models with distortion measurement errors," Statistical Papers, Springer, vol. 61(5), pages 2031-2057, October.
    5. Hao, Meiling & Lin, Yunyuan & Zhao, Xingqiu, 2016. "A relative error-based approach for variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 250-262.
    6. Zhenghui Feng & Jun Zhang & Qian Chen, 2020. "Statistical inference for linear regression models with additive distortion measurement errors," Statistical Papers, Springer, vol. 61(6), pages 2483-2509, December.
    7. Xia, Xiaochao & Liu, Zhi & Yang, Hu, 2016. "Regularized estimation for the least absolute relative error models with a diverging number of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 104-119.
    8. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    9. Chen, Kani & Lin, Yuanyuan & Wang, Zhanfeng & Ying, Zhiliang, 2016. "Least product relative error estimation," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 91-98.
    10. Zhang, Jun & Feng, Zhenghui & Peng, Heng, 2018. "Estimation and hypothesis test for partial linear multiplicative models," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 87-103.
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