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Classification Using Censored Functional Data

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  • Aurore Delaigle
  • Peter Hall

Abstract

We consider classification of functional data when the training curves are not observed on the same interval. Different types of classifier are suggested, one of which involves a new curve extension procedure. Our approach enables us to exploit the information contained in the endpoints of these intervals by incorporating it in an explicit but flexible way. We study asymptotic properties of our classifiers, and show that, in a variety of settings, they can even produce asymptotically perfect classification. The performance of our techniques is illustrated in applications to real and simulated data. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:504:p:1269-1283
    DOI: 10.1080/01621459.2013.824893
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    Cited by:

    1. Matthew W. Wheeler, 2019. "Bayesian additive adaptive basis tensor product models for modeling high dimensional surfaces: an application to high‐throughput toxicity testing," Biometrics, The International Biometric Society, vol. 75(1), pages 193-201, March.
    2. Kraus, David & Stefanucci, Marco, 2020. "Ridge reconstruction of partially observed functional data is asymptotically optimal," Statistics & Probability Letters, Elsevier, vol. 165(C).
    3. A. Delaigle & P. Hall, 2016. "Approximating fragmented functional data by segments of Markov chains," Biometrika, Biometrika Trust, vol. 103(4), pages 779-799.
    4. Mojirsheibani, Majid & Shaw, Crystal, 2018. "Classification with incomplete functional covariates," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 40-46.
    5. Chen, Lu-Hung & Jiang, Ci-Ren, 2018. "Sensible functional linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 39-52.
    6. 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.
    7. Elías Fernández, Antonio & Jiménez Recaredo, Raúl José, 2017. "Prediction Bands for Functional Data Based on Depth Measures," DES - Working Papers. Statistics and Econometrics. WS 24606, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Paganoni, Anna M. & Sangalli, Laura M., 2019. "A Depth for Censured Functional Data," DES - Working Papers. Statistics and Econometrics. WS 28579, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Sylvain Robbiano & Matthieu Saumard & Michel Curé, 2016. "Improving prediction performance of stellar parameters using functional models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1465-1476, June.
    10. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    11. 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.
    12. Park, Yeonjoo & Simpson, Douglas G., 2019. "Robust probabilistic classification applicable to irregularly sampled functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 37-49.
    13. 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.
    14. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    15. 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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