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The power divergence and the density power divergence families: the mathematical connection

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Abstract

The power divergence family of Cressie and Read (1984) is a highly popular family of density-based divergences which is widely used in robust parametric estimation and multinomial goodness-of-fit testing. This family forms a subclass of the family of ϕ-divergences (Csiszár, 1963; Pardo, 2006) or disparities (Lindsay, 1994). The more recently described family of density power divergences (Basu et al., 1998) is also extremely useful in robust parametric estimation. This paper explores the mathematical connection between these two families and establishes some interesting links.

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Authors and Affiliations

  1. Indian Statistical Institute, Kolkata, 700 108, India

    Sujayendu Patra, Avijit Maji & Ayanendranath Basu

  2. Complutense Universidad, Madrid, Spain

    Leandro Pardo

Authors
  1. Sujayendu Patra
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  2. Avijit Maji
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  3. Ayanendranath Basu
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  4. Leandro Pardo
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Correspondence to Ayanendranath Basu.

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Patra, S., Maji, A., Basu, A. et al. The power divergence and the density power divergence families: the mathematical connection. Sankhya B 75, 16–28 (2013). https://doi.org/10.1007/s13571-012-0050-3

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  • DOI: https://doi.org/10.1007/s13571-012-0050-3

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