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Partially Functional Linear Models with Linear Process Errors

Author

Listed:
  • Yanping Hu

    (School of Mathematical Sciences, Tongji University, Shanghai 200092, China)

  • Zhongqi Pang

    (Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China)

Abstract

In this paper, we focus on the partial functional linear model with linear process errors deduced by not necessarily independent random variables. Based on Mercer’s theorem and Karhunen–Loève expansion, we give the estimators of the slope parameter and coefficient function in the model, establish the asymptotic normality of the estimator for the parameter and discuss the weak convergence with rates of the proposed estimators. Meanwhile, the penalized estimator of the parameter is defined by the SCAD penalty and its oracle property is investigated. Finite sample behavior of the proposed estimators is also analysed via simulations.

Suggested Citation

  • Yanping Hu & Zhongqi Pang, 2023. "Partially Functional Linear Models with Linear Process Errors," Mathematics, MDPI, vol. 11(16), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3581-:d:1220071
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    References listed on IDEAS

    as
    1. Li, Yehua & Hsing, Tailen, 2007. "On rates of convergence in functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1782-1804, October.
    2. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
    3. Yao, Fang & Sue-Chee, Shivon & Wang, Fan, 2017. "Regularized partially functional quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 39-56.
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
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