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Choosing the most relevant level sets for depicting a sample of densities

Author

Listed:
  • Pedro Delicado

    (Universitat Politècnica de Catalunya)

  • Philippe Vieu

    (Université Paul Sabatier)

Abstract

When exploring a sample composed with a set of bivariate density functions, the question of the visualisation of the data has to front with the choice of the relevant level set(s). The approach proposed in this paper consists in defining the optimal level set(s) as being the one(s) allowing for the best reconstitution of the whole density. A fully data-driven procedure is developed in order to estimate the link between the level set(s) and their corresponding density, to construct optimal level set(s) and to choose automatically the number of relevant level set(s). The method is based on recent advances in functional data analysis when both response and predictors are functional. After a wide description of the methodology, finite sample studies are presented (including both real and simulated data) while theoretical studies are reported to a final appendix.

Suggested Citation

  • Pedro Delicado & Philippe Vieu, 2017. "Choosing the most relevant level sets for depicting a sample of densities," Computational Statistics, Springer, vol. 32(3), pages 1083-1113, September.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-017-0746-y
    DOI: 10.1007/s00180-017-0746-y
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    References listed on IDEAS

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    1. Germán Aneiros‐Pérez & Ricardo Cao & Juan M. Vilar‐Fernández, 2011. "Functional methods for time series prediction: a nonparametric approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(4), pages 377-392, July.
    2. Baíllo, Amparo & Cuesta-Albertos, Juan A. & Cuevas, Antonio, 2001. "Convergence rates in nonparametric estimation of level sets," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 27-35, May.
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    11. Delicado, Pedro & Vieu, Philippe, 2015. "Optimal level sets for bivariate density representation," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 1-18.
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    Cited by:

    1. S. Barahona & P. Centella & X. Gual-Arnau & M. V. Ibáñez & A. Simó, 2020. "Supervised classification of geometrical objects by integrating currents and functional data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 637-660, September.

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