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Dependence Assessment Based on Generalized Relative Complexity: Application to Sampling Network Design

Author

Listed:
  • F. J. Alonso

    (University of Granada)

  • M. C. Bueso

    (Technical University of Cartagena)

  • J. M. Angulo

    (University of Granada)

Abstract

Generalized statistical complexity measures provide a means to jointly quantify inner information and relative structural richness of a system described in terms of a probability model. As a natural divergence-based extension in this context, generalized relative complexity measures have been proposed for the local comparison of two given probability distributions. In this paper, the behavior of generalized relative complexity measures is studied for assessment of structural dependence in a random vector leading to a concept of ‘generalized mutual complexity’. A related optimality criterion for sampling network design, which provides an alternative to mutual information based methods in the complexity context, is formulated. Aspects related to practical implementation, and conceptual issues regarding the meaning and potential use of this approach, are discussed. Numerical examples are used for illustration.

Suggested Citation

  • F. J. Alonso & M. C. Bueso & J. M. Angulo, 2016. "Dependence Assessment Based on Generalized Relative Complexity: Application to Sampling Network Design," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 921-933, September.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:3:d:10.1007_s11009-016-9495-6
    DOI: 10.1007/s11009-016-9495-6
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    References listed on IDEAS

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    1. Caselton, W. F. & Zidek, J. V., 1984. "Optimal monitoring network designs," Statistics & Probability Letters, Elsevier, vol. 2(4), pages 223-227, August.
    2. Zdravko I. Botev & Dirk P. Kroese, 2011. "The Generalized Cross Entropy Method, with Applications to Probability Density Estimation," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 1-27, March.
    3. Martin, M.T. & Plastino, A. & Rosso, O.A., 2006. "Generalized statistical complexity measures: Geometrical and analytical properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 439-462.
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    Cited by:

    1. Angulo, J. & Angulo, J.C. & Angulo, J.M., 2018. "An application of information theory to stochastic classical gravitational fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 129-141.

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