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Kernel depth funcions for functional data

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  • Hernández Banadik, Nicolás Jorge
  • Muñoz García, Alberto

Abstract

In the last years the concept of data depth has been increasingly used in Statistics as a center-outward ordering of sample points in multivariate data sets. Recently data depth has been extended to functional data. In this paper we propose new intrinsic functional data depths based on the representation of functional data on Reproducing Kernel Hilbert Spaces, and test its performance against a number of well known alternatives in the problem of functional outlier detection.

Suggested Citation

  • Hernández Banadik, Nicolás Jorge & Muñoz García, Alberto, 2017. "Kernel depth funcions for functional data," DES - Working Papers. Statistics and Econometrics. WS 24615, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:24615
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    1. Anirvan Chakraborty & Probal Chaudhuri, 2014. "On data depth in infinite dimensional spaces," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 303-324, April.
    2. 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.
    3. 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.
    4. 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.
    5. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4979-4988, July.
    6. López-Pintado, Sara & Romo, Juan, 2011. "A half-region depth for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1679-1695, April.
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    Kernel depth;

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