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Linear manifold modeling and graph estimation based on multivariate functional data with different coarseness scales

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  • Pircalabelu, Eugen

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Claeskens, Gerda

    (KU Leuven)

Abstract

We develop a high-dimensional graphical modeling approach for functional data where the number of functions exceeds the available sample size. This is accomplished by proposing a sparse estimator for a concentration matrix when identifying linear manifolds. As such, the procedure extends the ideas of the manifold representation for functional data to high-dimensional settings where the number of functions is larger than the sample size. By working in a penalized framework it enriches the functional data framework by estimating sparse undirected graphs that show how functional nodes connect to other functional nodes. The procedure allows multiple coarseness scales to be present in the data and proposes a simultaneous estimation of several related graphs.

Suggested Citation

  • Pircalabelu, Eugen & Claeskens, Gerda, 2021. "Linear manifold modeling and graph estimation based on multivariate functional data with different coarseness scales," LIDAM Discussion Papers ISBA 2021032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2021032
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    References listed on IDEAS

    as
    1. Xinghao Qiao & Shaojun Guo & Gareth M. James, 2019. "Functional Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 211-222, January.
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    3. Pircalabelu, Eugen & Claeskens, Gerda & Jahfari, Sara & Waldorp, Lourens J., 2015. "A focused information criterion for graphical models in fMRI connectivity with high-dimensional data," LIDAM Reprints ISBA 2015045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Jeng-Min Chiou & Hans-Georg Müller, 2014. "Linear manifold modelling of multivariate functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 605-626, June.
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    6. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    7. Pircalabelu, Eugen & Claeskens, Gerda & Waldorp, Lourens J., 2016. "Mixed scale joint graphical lasso," LIDAM Reprints ISBA 2016049, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
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    10. Pircalabelu, Eugen & Claeskens, Gerda & Waldorp, Lourens J., 2015. "A focused information criterion for graphical models," LIDAM Reprints ISBA 2015044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    More about this item

    Keywords

    Multivariate functional data; Multiscale data; Graphical lasso; Joint estimation; Group penalty;
    All these keywords.

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