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Relationship Between Kendall's tau Correlation and Mutual Information

  • Autores: Mohammad Bolbolian Ghalibaf
  • Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 43, Nº. 1, 2020, págs. 3-20
  • Idioma: inglés
  • DOI: 10.15446/rce.v43n1.78054
  • Títulos paralelos:
    • Relación entre la correlación tau de Kendall e información mutua
  • Enlaces
  • Resumen
    • español

      Resumen La información mutua (MI) puede ser vista como una medida de asociación multivariante en un vector aleatorio. Sin embargo, la estimación de MI es difícil ya que la estimación de la función de densidad de probabilidad conjunta (PDF) de datos distribuidos no gaussianos es un problema difícil. La función copula es una herramienta apropiada para estimar el MI ya que la función de densidad de probabilidad de las variables aleatorias se puede expresar como el producto de la función de densidad de cópula asociada y de los PDF marginales. Con una pequeña búsqueda, encontramos que la información mutua propuesta basada en cópulas es mucho más precisa que los métodos convencionales, como el histograma de la articulación y el MI basado en ventana de Parzen. En este artículo, al utilizar el método basado en cópulas, calculamos el MI para algunas familias de funciones de distribución bivariadas y estudiamos la relación entre la correlación tau de Kendall y el MI de las distribuciones bivariadas. Finalmente, usando un conjunto de datos real, ilustramos la eficiencia de este enfoque.

    • English

      Abstract Mutual information (MI) can be viewed as a measure of multivariate association in a random vector. However, the estimation of MI is difficult since the estimation of the joint probability density function (PDF) of non-Gaussian distributed data is a hard problem. Copula function is an appropriate tool for estimating MI since the joint probability density function of random variables can be expressed as the product of the associated copula density function and marginal PDF's. With a little search, we find that the proposed copulas-based mutual information is much more accurate than conventional methods such as the joint histogram and Parzen window-based MI. In this paper, by using the copulas-based method, we compute MI for some family of bivariate distribution functions and study the relationship between Kendall's tau correlation and MI of bivariate distributions. Finally, using a real dataset, we illustrate the efficiency of this approach.

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