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Convergence of parameter estimation of a Gaussian mixture model minimizing the Gini index of dissimilarity

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  • Adriana Laura López Lobato
  • Martha Lorena Avendaño Garrido

Abstract

The Gaussian mixture model (GMM) is a probabilistic model that represents the behavior of a data set as a linear combination of K Gaussian densities. The most used method to estimate the parameters of a GMM is the maximum likelihood, giving rise to the EM-algorithm. Another alternative is minimizing the Gini index of dissimilarity between the empirical distribution of the observed data and the parametric distribution GMM, deriving in an iterative algorithm called GID-algorithm. In this work, we prove its convergence with the help of the χ2 divergence.

Suggested Citation

  • Adriana Laura López Lobato & Martha Lorena Avendaño Garrido, 2024. "Convergence of parameter estimation of a Gaussian mixture model minimizing the Gini index of dissimilarity," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(17), pages 6030-6037, September.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:17:p:6030-6037
    DOI: 10.1080/03610926.2023.2239396
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