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

Adriana Laura López Lobato and Martha Lorena Avendaño Garrido

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 17, 6030-6037

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.

Date: 2024
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DOI: 10.1080/03610926.2023.2239396

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