IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i9p3452-3465.html
   My bibliography  Save this article

Structural components in functional data

Author

Listed:
  • Park, Juhyun
  • Gasser, Theo
  • Rousson, Valentin

Abstract

Analyzing functional data often leads to finding common factors, for which functional principal component analysis proves to be a useful tool to summarize and characterize the random variation in a function space. The representation in terms of eigenfunctions is optimal in the sense of L2 approximation. However, the eigenfunctions are not always directed towards an interesting and interpretable direction in the context of functional data and thus could obscure the underlying structure. To overcome such difficulty, an alternative to functional principal component analysis is proposed that produces directed components which may be more informative and easier to interpret. These structural components are similar to principal components, but are adapted to situations in which the domain of the function may be decomposed into disjoint intervals such that there is effectively independence between intervals and positive correlation within intervals. The approach is demonstrated with synthetic examples as well as real data. Properties for special cases are also studied.

Suggested Citation

  • Park, Juhyun & Gasser, Theo & Rousson, Valentin, 2009. "Structural components in functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3452-3465, July.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3452-3465
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00068-1
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ferraty, Frederic & Vieu, Philippe & Viguier-Pla, Sylvie, 2007. "Factor-based comparison of groups of curves," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4903-4910, June.
    2. Fang Yao & Hans-Georg Müller & Andrew J. Clifford & Steven R. Dueker & Jennifer Follett & Yumei Lin & Bruce A. Buchholz & John S. Vogel, 2003. "Shrinkage Estimation for Functional Principal Component Scores with Application to the Population Kinetics of Plasma Folate," Biometrics, The International Biometric Society, vol. 59(3), pages 676-685, September.
    3. Wu H. & Zhang J-T., 2002. "Local Polynomial Mixed-Effects Models for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 883-897, September.
    4. Mante, Claude & Yao, Anne-Francoise & Degiovanni, Claude, 2007. "Principal component analysis of measures, with special emphasis on grain-size curves," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4969-4983, June.
    5. Gervini D. & Rousson V., 2004. "Criteria for Evaluating Dimension-Reducing Components for Multivariate Data," The American Statistician, American Statistical Association, vol. 58, pages 72-76, February.
    6. Nerini, David & Ghattas, Badih, 2007. "Classifying densities using functional regression trees: Applications in oceanology," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4984-4993, June.
    7. Chiou, Jeng-Min & Muller, Hans-Georg, 2007. "Diagnostics for functional regression via residual processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4849-4863, June.
    8. 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.
    9. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    10. Valentin Rousson & Theo Gasser, 2004. "Simple component analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(4), pages 539-555, November.
    11. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    12. Ruiz-Medina, M.D. & Salmeron, R. & Angulo, J.M., 2007. "Kalman filtering from POP-based diagonalization of ARH(1)," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4994-5008, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Martínez-Camblor, Pablo & Corral, Norberto, 2011. "Repeated measures analysis for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3244-3256, December.
    2. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    3. Rachdi, Mustapha & Laksaci, Ali & Demongeot, Jacques & Abdali, Abdel & Madani, Fethi, 2014. "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 53-68.
    4. Boj, Eva & Delicado, Pedro & Fortiana, Josep, 2010. "Distance-based local linear regression for functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 429-437, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. van der Linde, Angelika, 2008. "Variational Bayesian functional PCA," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 517-533, December.
    2. Beran, Jan & Liu, Haiyan, 2016. "Estimation of eigenvalues, eigenvectors and scores in FDA models with dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 218-233.
    3. Kyunghee Han & Pantelis Z Hadjipantelis & Jane-Ling Wang & Michael S Kramer & Seungmi Yang & Richard M Martin & Hans-Georg Müller, 2018. "Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-18, November.
    4. Kehui Chen & Xiaoke Zhang & Alexander Petersen & Hans-Georg Müller, 2017. "Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 582-604, December.
    5. Graciela Boente & Daniela Rodriguez & Mariela Sued, 2018. "Testing equality between several populations covariance operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 919-950, August.
    6. Peter Hall & Hans‐Georg Müller & Fang Yao, 2008. "Modelling sparse generalized longitudinal observations with latent Gaussian processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 703-723, September.
    7. Şentürk, Damla & Ghosh, Samiran & Nguyen, Danh V., 2014. "Exploratory time varying lagged regression: Modeling association of cognitive and functional trajectories with expected clinic visits in older adults," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 1-15.
    8. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    9. Guangxing Wang & Sisheng Liu & Fang Han & Chong‐Zhi Di, 2023. "Robust functional principal component analysis via a functional pairwise spatial sign operator," Biometrics, The International Biometric Society, vol. 79(2), pages 1239-1253, June.
    10. Poskitt, D.S. & Sengarapillai, Arivalzahan, 2013. "Description length and dimensionality reduction in functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 98-113.
    11. Ci-Ren Jiang & John A. D. Aston & Jane-Ling Wang, 2016. "A Functional Approach to Deconvolve Dynamic Neuroimaging Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 1-13, March.
    12. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    13. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    14. Tomáš Rubín & Victor M. Panaretos, 2020. "Functional lagged regression with sparse noisy observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 858-882, November.
    15. Orlando Joaqui-Barandica & Diego F. Manotas-Duque, 2023. "How do Climate and Macroeconomic Factors Affect the Profitability of the Energy Sector?," International Journal of Energy Economics and Policy, Econjournals, vol. 13(4), pages 444-454, July.
    16. Nie, Yunlong & Cao, Jiguo, 2020. "Sparse functional principal component analysis in a new regression framework," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    17. Cees Diks & Bram Wouters, 2023. "Noise reduction for functional time series," Papers 2307.02154, arXiv.org.
    18. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2019. "The spatial sign covariance operator: Asymptotic results and applications," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 115-128.
    19. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2010. "Inference under functional proportional and common principal component models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 464-475, February.
    20. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3452-3465. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.