IDEAS home Printed from
   My bibliography  Save this article

Spatial functional normal mixed effect approach for curve classification


  • Maria Ruiz-Medina


  • Rosa Espejo
  • Elvira Romano


This paper proposes a spatial functional formulation of the normal mixed effect model for the statistical classification of spatially dependent Gaussian curves, in both parametric and state space model frameworks. Fixed effect parameters are represented in terms of a functional multiple regression model whose regression operators can change in space. Local spatial homogeneity of these operators is measured in terms of their Hilbert–Schmidt distances, leading to the classification of fixed effect curves in different groups. Assuming that the Gaussian random effect curves obey a spatial autoregressive dynamics of order one [SARH(1) dynamics], a second functional classification criterion is proposed in order to detect local spatially homogeneous patterns in the mean quadratic functional variation of Gaussian random effect curve increments. Finally, the two criteria are combined to detect local spatially homogeneous patterns in the regression operators and in the functional mean quadratic variation, under a state space approach. A real data example in the financial context is analyzed as an illustration. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Maria Ruiz-Medina & Rosa Espejo & Elvira Romano, 2014. "Spatial functional normal mixed effect approach for curve classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 257-285, September.
  • Handle: RePEc:spr:advdac:v:8:y:2014:i:3:p:257-285
    DOI: 10.1007/s11634-014-0174-6

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    1. M. Giacofci & S. Lambert-Lacroix & G. Marot & F. Picard, 2013. "Wavelet-Based Clustering for Mixed-Effects Functional Models in High Dimension," Biometrics, The International Biometric Society, vol. 69(1), pages 31-40, March.
    2. Jeng-Min Chiou & Pai-Ling Li, 2007. "Functional clustering and identifying substructures of longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 679-699.
    3. Hans Degryse & Peter Goeij & Peter Kappert, 2012. "The impact of firm and industry characteristics on small firms’ capital structure," Small Business Economics, Springer, vol. 38(4), pages 431-447, May.
    4. Alonso, Andrés M. & Casado, David & Romo, Juan, 2012. "Supervised classification for functional data: A weighted distance approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2334-2346.
    5. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    6. A. Delaigle & P. Hall & N. Bathia, 2012. "Componentwise classification and clustering of functional data," Biometrika, Biometrika Trust, vol. 99(2), pages 299-313.
    7. Ruiz-Medina, M.D., 2011. "Spatial autoregressive and moving average Hilbertian processes," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 292-305, February.
    8. Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
    9. Laurence Booth, 2001. "Capital Structures in Developing Countries," Journal of Finance, American Finance Association, vol. 56(1), pages 87-130, February.
    10. Li, Bin & Yu, Qingzhao, 2008. "Classification of functional data: A segmentation approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4790-4800, June.
    11. C. Abraham & P. A. Cornillon & E. Matzner-Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B-Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595.
    12. Angelini, Claudia & De Canditiis, Daniela & Leblanc, Frédérique, 2003. "Wavelet regression estimation in nonparametric mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 267-291, May.
    13. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    14. M. Aguilera-Morillo & Ana Aguilera & Manuel Escabias & Mariano Valderrama, 2013. "Penalized spline approaches for functional logit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 251-277, June.
    15. repec:taf:gnstxx:v:22:y:2010:i:4:p:477-497 is not listed on IDEAS
    16. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. repec:spr:alstar:v:102:y:2018:i:1:d:10.1007_s10182-016-0280-1 is not listed on IDEAS


    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:spr:advdac:v:8:y:2014:i:3:p:257-285. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.