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The $$\hbox {DD}^G$$ DD G -classifier in the functional setting

Author

Listed:
  • J. A. Cuesta-Albertos

    (University of Cantabria)

  • M. Febrero-Bande

    (University of Santiago de Compostela)

  • M. Oviedo de la Fuente

    (University of Santiago de Compostela)

Abstract

The maximum depth classifier was the first attempt to use data depths instead of multivariate raw data in classification problems. Recently, the DD-classifier has addressed some of the serious limitations of this classifier but issues still remain. This paper aims to extend the DD-classifier as follows: first, by enabling it to handle more than two groups; second, by applying regular classification methods (such as kNN, linear or quadratic classifiers, recursive partitioning, etc) to DD-plots, which is particularly useful, because it gives insights based on the diagnostics of these methods; and third, by integrating various sources of information (data depths, multivariate functional data, etc) in the classification procedure in a unified way. This paper also proposes an enhanced revision of several functional data depths and it provides a simulation study and applications to some real data sets.

Suggested Citation

  • J. A. Cuesta-Albertos & M. Febrero-Bande & M. Oviedo de la Fuente, 2017. "The $$\hbox {DD}^G$$ DD G -classifier in the functional setting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 119-142, March.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0502-6
    DOI: 10.1007/s11749-016-0502-6
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    References listed on IDEAS

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    1. Gerda Claeskens & Mia Hubert & Leen Slaets & Kaveh Vakili, 2014. "Multivariate Functional Halfspace Depth," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 411-423, March.
    2. Aurore Delaigle & Peter Hall, 2012. "Achieving near perfect classification for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 267-286, March.
    3. Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
    4. repec:cte:wsrepe:ws131312 is not listed on IDEAS
    5. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2004. "An anova test for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 111-122, August.
    6. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    7. Carlo Sguera & Pedro Galeano & Rosa Lillo, 2014. "Spatial depth-based classification for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 725-750, December.
    8. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    9. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    10. Manuel Febrero-Bande & Wenceslao González-Manteiga, 2013. "Generalized additive models for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 278-292, June.
    11. Jun Li & Juan A. Cuesta-Albertos & Regina Y. Liu, 2012. "DD -Classifier: Nonparametric Classification Procedure Based on DD -Plot," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 737-753, June.
    12. Székely, Gábor J. & Rizzo, Maria L., 2013. "The distance correlation t-test of independence in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 193-213.
    13. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    14. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
    15. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    16. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
    17. Anil K. Ghosh & Probal Chaudhuri, 2005. "On Maximum Depth and Related Classifiers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 327-350, June.
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