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Approximating fragmented functional data by segments of Markov chains

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  • A. Delaigle
  • P. Hall

Abstract

We consider curve extension and linear prediction for functional data observed only on a part of their domain, in the form of fragments. We suggest an approach based on a combination of Markov chains and nonparametric smoothing techniques, which enables us to extend the observed fragments and construct approximated prediction intervals around them, construct mean and covariance function estimators, and derive a linear predictor. The procedure is illustrated on real and simulated data.

Suggested Citation

  • A. Delaigle & P. Hall, 2016. "Approximating fragmented functional data by segments of Markov chains," Biometrika, Biometrika Trust, vol. 103(4), pages 779-799.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:4:p:779-799.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw040
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    References listed on IDEAS

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    1. Lee, Eun Ryung & Park, Byeong U., 2012. "Sparse estimation in functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 1-17.
    2. Jan G. De Gooijer & Dawit Zerom, 2003. "On Conditional Density Estimation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(2), pages 159-176, May.
    3. Liebl, Dominik, 2013. "Modeling and Forecasting Electricity Spot Prices: A Functional Data Perspective," MPRA Paper 50881, University Library of Munich, Germany.
    4. 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.
    5. 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.
    6. Apanasovich, Tatiyana V. & Goldstein, Edward, 2008. "On prediction error in functional linear regression," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1807-1810, September.
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    Cited by:

    1. 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.
    2. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    3. 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.
    4. 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.
    5. Kraus, David & Stefanucci, Marco, 2020. "Ridge reconstruction of partially observed functional data is asymptotically optimal," Statistics & Probability Letters, Elsevier, vol. 165(C).
    6. 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.
    7. 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.

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