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Estimation for Partial Functional Multiplicative Regression Model

Author

Listed:
  • Xiaojing Liu

    (School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 031031, China)

  • Ping Yu

    (School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 031031, China)

  • Jianhong Shi

    (School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 031031, China)

Abstract

Functional data such as curves, shapes, and manifolds have become more and more common with modern technological advancements. The multiplicative regression model is well suited for analyzing data with positive responses. In this study, we study the estimation problems of the partial functional multiplicative regression model (PFMRM) based on the least absolute relative error (LARE) criterion and least product relative error (LPRE) criterion. The functional predictor and slope function are approximated by the functional principal component basis functions. Under certain regularity conditions, we derive the convergence rate of the slope function and establish the asymptotic normality of the slope vector for two estimation methods. Monte Carlo simulations are carried out to evaluate the proposed methods, and an application to Tecator data is investigated for illustration.

Suggested Citation

  • Xiaojing Liu & Ping Yu & Jianhong Shi, 2025. "Estimation for Partial Functional Multiplicative Regression Model," Mathematics, MDPI, vol. 13(3), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:471-:d:1581179
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Tao Zhang & Qingzhao Zhang & Naixiong Li, 2016. "Least absolute relative error estimation for functional quadratic multiplicative model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5802-5817, October.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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