IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v48y2000i4p335-345.html
   My bibliography  Save this article

Kernel-based functional principal components

Author

Listed:
  • Boente, Graciela
  • Fraiman, Ricardo

Abstract

In this paper, we propose kernel-based smooth estimates of the functional principal components when data are continuous trajectories of stochastic processes. Strong consistency and the asymptotic distribution are derived under mild conditions.

Suggested Citation

  • Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    • Handle: RePEc:eee:stapro:v:48:y:2000:i:4:p:335-345
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(00)00014-6
    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. Philippe Besse & J. Ramsay, 1986. "Principal components analysis of sampled functions," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 285-311, June.
    2. 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.
    3. Fraiman, Ricardo & Iribarren, Gonzalo Pérez, 1991. "Nonparametric regression estimation in models with weak error's structure," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 180-196, May.
    4. J. Ramsay, 1982. "When the data are functions," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 379-396, December.
    5. Yurinskii, V. V., 1976. "Exponential inequalities for sums of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 473-499, December.
    Full references (including those not matched with items on IDEAS)

    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. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
    2. Christoph Hellmayr & Alan E. Gelfand, 2021. "A Partition Dirichlet Process Model for Functional Data Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 30-65, May.
    3. Panaretos, Victor M. & Tavakoli, Shahin, 2013. "Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2779-2807.
    4. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    5. Jakub Poręba & Jerzy Baranowski, 2022. "Functional Logistic Regression for Motor Fault Classification Using Acoustic Data in Frequency Domain," Energies, MDPI, vol. 15(15), pages 1-12, July.
    6. Christian Acal & Ana M. Aguilera & Manuel Escabias, 2020. "New Modeling Approaches Based on Varimax Rotation of Functional Principal Components," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    7. Ferraty, F. & Van Keilegom, I. & Vieu, P., 2012. "Regression when both response and predictor are functions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 10-28.
    8. Huang, Su-Yun & Lu, Henry Horng-Shing, 2001. "Extended Gauss-Markov Theorem for Nonparametric Mixed-Effects Models," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 249-266, February.
    9. 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.
    10. 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.
    11. Lakraj, Gamage Pemantha & Ruymgaart, Frits, 2017. "Some asymptotic theory for Silverman’s smoothed functional principal components in an abstract Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 122-132.
    12. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 1-73, June.
    13. Cardot, Hervé & Sarda, Pacal, 2005. "Estimation in generalized linear models for functional data via penalized likelihood," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 24-41, January.
    14. Hlubinka, Daniel & Prchal, Lubos, 2007. "Changes in atmospheric radiation from the statistical point of view," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4926-4941, June.
    15. Hans-Georg Müller & Wenjing Yang, 2010. "Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-29, May.
    16. van Delft, Anne & Eichler, Michael, 2017. "Locally Stationary Functional Time Series," LIDAM Discussion Papers ISBA 2017023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. repec:eca:wpaper:2013/131191 is not listed on IDEAS
    18. Mingotti, Nicola & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2015. "A Random Walk Test for Functional Time Series," DES - Working Papers. Statistics and Econometrics. WS ws1506, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. María Edo & Walter Sosa Escudero & Marcela Svarc, 2021. "A multidimensional approach to measuring the middle class," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(1), pages 139-162, March.
    20. 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.
    21. Cristhian Leonardo Urbano-Leon & Manuel Escabias & Diana Paola Ovalle-Muñoz & Javier Olaya-Ochoa, 2023. "Scalar Variance and Scalar Correlation for Functional Data," Mathematics, MDPI, vol. 11(6), pages 1-20, March.

    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:stapro:v:48:y:2000:i:4:p:335-345. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.