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Linear manifold modelling of multivariate functional data

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  • Jeng-Min Chiou
  • Hans-Georg Müller

Abstract

type="main" xml:id="rssb12038-abs-0001"> Multivariate functional data are increasingly encountered in data analysis, whereas statistical models for such data are not well developed yet. Motivated by a case-study where one aims to quantify the relationship between various longitudinally recorded behaviour intensities for Drosophila flies, we propose a functional linear manifold model. This model reflects the functional dependence between the components of multivariate random processes and is defined through data-determined linear combinations of the multivariate component trajectories, which are characterized by a set of varying-coefficient functions. The time varying linear relationships that govern the components of multivariate random functions yield insights about the underlying processes and also lead to noise-reduced representations of the multivariate component trajectories. The functional linear manifold model proposed is put to the task for an analysis of longitudinally observed behavioural patterns of flying, feeding, walking and resting over the lifespan of Drosophila flies and is also investigated in simulations.

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  • 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.
    • Handle: RePEc:bla:jorssb:v:76:y:2014:i:3:p:605-626
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.76.issue-3
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    Cited by:

    1. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    2. Jialiang Li & Yaguang Li & Tailen Hsing, 2022. "On functional processes with multiple discontinuities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 933-972, July.
    3. Yuan Gao & Han Lin Shang, 2017. "Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates," Risks, MDPI, vol. 5(2), pages 1-18, March.
    4. 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).
    5. Fangting Zhou & Kejun He & Kunbo Wang & Yanxun Xu & Yang Ni, 2023. "Functional Bayesian networks for discovering causality from multivariate functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3279-3293, December.
    6. Ruonan Li & Luo Xiao, 2023. "Latent factor model for multivariate functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3307-3318, December.

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