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PCA‐based discrimination of partially observed functional data, with an application to AneuRisk65 data set

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  • Marco Stefanucci
  • Laura M. Sangalli
  • Pierpaolo Brutti

Abstract

Functional data are usually assumed to be observed on a common domain. However, it is often the case that some portion of the functional data is missing for some statistical unit, invalidating most of the existing techniques for functional data analysis. The development of methods able to handle partially observed or incomplete functional data is currently attracting increasing interest. We here briefly review this literature. We then focus on discrimination based on principal component analysis and illustrate a few possible methods via simulation studies and an application to the AneuRisk65 data set. We show that carrying out the analysis over the full domain, where at least one of the functional data is observed, may not be the optimal choice for classification purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:72:y:2018:i:3:p:246-264
    DOI: 10.1111/stan.12137
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    References listed on IDEAS

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    1. Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Veneziani, Alessandro, 2009. "A Case Study in Exploratory Functional Data Analysis: Geometrical Features of the Internal Carotid Artery," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 37-48.
    2. Floriello, Davide & Vitelli, Valeria, 2017. "Sparse clustering of functional data," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 1-18.
    3. F. Ferraty & P. Hall & P. Vieu, 2010. "Most-predictive design points for functional data predictors," Biometrika, Biometrika Trust, vol. 97(4), pages 807-824.
    4. Liebl, Dominik, 2013. "Modeling and Forecasting Electricity Spot Prices: A Functional Data Perspective," MPRA Paper 50881, University Library of Munich, Germany.
    5. A. Delaigle & P. Hall & N. Bathia, 2012. "Componentwise classification and clustering of functional data," Biometrika, Biometrika Trust, vol. 99(2), pages 299-313.
    6. 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.
    7. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    8. Aurore Delaigle & Peter Hall, 2013. "Classification Using Censored Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1269-1283, December.
    9. A. Delaigle & P. Hall, 2016. "Approximating fragmented functional data by segments of Markov chains," Biometrika, Biometrika Trust, vol. 103(4), pages 779-799.
    10. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
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    Cited by:

    1. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    2. Kraus, David & Stefanucci, Marco, 2020. "Ridge reconstruction of partially observed functional data is asymptotically optimal," Statistics & Probability Letters, Elsevier, vol. 165(C).
    3. Jianing Fan & Hans‐Georg Müller, 2022. "Conditional distribution regression for functional responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 502-524, June.

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