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Covariance estimation error of incomplete functional data under RKHS framework

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  • Yao, Binhong
  • Li, Peixing

Abstract

In recent years, functional data analysis (FDA) and reproducing kernel Hilbert space (RKHS) are frequently encountered in various applications. However, employing the RKHS framework to study the covariance of incomplete functional data is rare. In this paper, we consider the global estimation error of the covariance function obtained by fragment data. Our theorem is built on the connection between functional data and RKHS, by using the covariance function as the reproducing kernel. We take the mean square integrability of functional data into consideration, and ease the previous restrictions of covariance function and observation area. Simulation results show the veracity of our theoretical finding by comparing the error of two kinds of functional data in covariance estimation. The existing N resolution patched (N-rp) method to estimate covariance in a local observation area has been improved, resulting in a considerable reduction in computing costs.

Suggested Citation

  • Yao, Binhong & Li, Peixing, 2023. "Covariance estimation error of incomplete functional data under RKHS framework," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    • Handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322007809
    DOI: 10.1016/j.amc.2022.127712
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    References listed on IDEAS

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    1. Song, Jun & Li, Bing, 2021. "Nonlinear and additive principal component analysis for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    2. Luo Xiao & Yingxing Li & David Ruppert, 2013. "Fast bivariate P-splines: the sandwich smoother," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 577-599, June.
    3. José R. Berrendero & Antonio Cuevas & José L. Torrecilla, 2018. "On the Use of Reproducing Kernel Hilbert Spaces in Functional Classification," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1210-1218, July.
    4. Liebl, Dominik & Rameseder, Stefan, 2019. "Partially observed functional data: The case of systematically missing parts," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 104-115.
    5. repec:wyi:journl:002174 is not listed on IDEAS
    6. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 231-255, September.
    7. Cui, Xia & Lin, Hongmei & Lian, Heng, 2020. "Partially functional linear regression in reproducing kernel Hilbert spaces," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    8. David Kraus, 2015. "Components and completion of partially observed functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 777-801, September.
    9. M-H Descary & V M Panaretos, 2019. "Recovering covariance from functional fragments," Biometrika, Biometrika Trust, vol. 106(1), pages 145-160.
    10. J. Ramsay, 1982. "When the data are functions," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 379-396, December.
    11. Manuel Febrero-Bande & Pedro Galeano & Wenceslao González-Manteiga, 2017. "Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study," International Statistical Review, International Statistical Institute, vol. 85(1), pages 61-83, April.
    12. M. Abeidallah & B. Mechab & T. Merouan, 2020. "Local linear estimate of the point at high risk: Spatial functional data case," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(11), pages 2561-2584, June.
    13. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
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