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Partially functional linear regression in reproducing kernel Hilbert spaces

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  • Cui, Xia
  • Lin, Hongmei
  • Lian, Heng

Abstract

In this paper, we study the partially functional linear regression model in which there are both functional predictors and traditional multivariate predictors. The existing approach is based on approximation using functional principal component analysis which has some limitations. We propose an alternative framework based on reproducing kernel Hilbert spaces (RKHS) which has not been investigated in the literature for the partially functional case. Asymptotic normality of the non-functional part is also shown. Even when reduced to the purely functional linear regression, our results extend the existing results in two aspects: rates are established using both prediction risk and RKHS norm, and faster rates are possible if greater smoothness is assumed. Some simulations are used to demonstrate the performance of the proposed estimator.

Suggested Citation

  • Cui, Xia & Lin, Hongmei & Lian, Heng, 2020. "Partially functional linear regression in reproducing kernel Hilbert spaces," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:csdana:v:150:y:2020:i:c:s0167947320300694
    DOI: 10.1016/j.csda.2020.106978
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    1. Jeng‐Min Chiou & Pai‐Ling Li, 2007. "Functional clustering and identifying substructures of longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 679-699, September.
    2. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    3. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    4. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    5. Ma, Ping & Zhong, Wenxuan, 2008. "Penalized Clustering of Large-Scale Functional Data With Multiple Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 625-636, June.
    6. Xiaoxiao Sun & Pang Du & Xiao Wang & Ping Ma, 2018. "Optimal Penalized Function-on-Function Regression Under a Reproducing Kernel Hilbert Space Framework," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1601-1611, October.
    7. Raymond K. W. Wong & Yehua Li & Zhengyuan Zhu, 2019. "Partially Linear Functional Additive Models for Multivariate Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 406-418, January.
    8. Aurore Delaigle & Peter Hall, 2012. "Achieving near perfect classification for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 267-286, March.
    9. 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.
    10. Lian, Heng, 2015. "Minimax prediction for functional linear regression with functional responses in reproducing kernel Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 395-402.
    11. J. Ramsay, 1982. "When the data are functions," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 379-396, December.
    12. Cristian Preda & Gilbert Saporta & Caroline Lévéder, 2007. "PLS classification of functional data," Computational Statistics, Springer, vol. 22(2), pages 223-235, July.
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    Cited by:

    1. Yao, Binhong & Li, Peixing, 2023. "Covariance estimation error of incomplete functional data under RKHS framework," Applied Mathematics and Computation, Elsevier, vol. 443(C).

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