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Ridge reconstruction of partially observed functional data is asymptotically optimal

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  • Kraus, David
  • Stefanucci, Marco

Abstract

When functional data are observed on parts of the domain, it is of interest to recover the missing parts of curves. Kraus (2015) proposed a linear reconstruction method based on ridge regularization. Kneip and Liebl (2019) argue that an assumption under which Kraus (2015) established the consistency of the ridge method is too restrictive and propose a principal component reconstruction method that they prove to be asymptotically optimal. In this note we relax the restrictive assumption that the true best linear reconstruction operator is Hilbert–Schmidt and prove that the ridge method achieves asymptotic optimality under essentially no assumptions. The result is illustrated in a simulation study.

Suggested Citation

  • Kraus, David & Stefanucci, Marco, 2020. "Ridge reconstruction of partially observed functional data is asymptotically optimal," Statistics & Probability Letters, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:stapro:v:165:y:2020:i:c:s0167715220301164
    DOI: 10.1016/j.spl.2020.108813
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    References listed on IDEAS

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    1. Bugni, Federico A., 2012. "Specification Test For Missing Functional Data," Econometric Theory, Cambridge University Press, vol. 28(5), pages 959-1002, October.
    2. 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.
    3. Liebl, Dominik, 2013. "Modeling and Forecasting Electricity Spot Prices: A Functional Data Perspective," MPRA Paper 50881, University Library of Munich, Germany.
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    7. David Kraus & Marco Stefanucci, 2019. "Classification of functional fragments by regularized linear classifiers with domain selection," Biometrika, Biometrika Trust, vol. 106(1), pages 161-180.
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    10. Mojirsheibani, Majid & Shaw, Crystal, 2018. "Classification with incomplete functional covariates," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 40-46.
    11. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    12. Marco Stefanucci & Laura M. Sangalli & Pierpaolo Brutti, 2018. "PCA‐based discrimination of partially observed functional data, with an application to AneuRisk65 data set," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 246-264, August.
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    Cited by:

    1. Antonio Elías & Raúl Jiménez & Han Lin Shang, 2023. "Depth-based reconstruction method for incomplete functional data," Computational Statistics, Springer, vol. 38(3), pages 1507-1535, September.

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