{"ID":2854531,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.14482","arxiv_id":"2510.14482","title":"Strong consistency of pseudo-likelihood parameter estimator for univariate Gaussian mixture models","abstract":"We consider a new method for estimating the parameters of univariate Gaussian mixture models. The method relies on a nonparametric density estimator $\\hat{f}_n$ (typically a kernel estimator). For every set of Gaussian mixture components, $\\hat{f}_n$ is used to find the best set of mixture weights. That set is obtained by minimizing the $L_2$ distance between $\\hat{f}_n$ and the Gaussian mixture density with the given component parameters. The densities together with the obtained weights are then plugged in to the likelihood function, resulting in the so-called pseudo-likelihood function. The final parameter estimators are the parameter values that maximize the pseudo-likelihood function together with the corresponding weights. The advantages of the pseudo-likelihood over the full likelihood are: 1) its arguments are the means and variances only, mixture weights are also functions of the means and variances; 2) unlike the likelihood function, it is always bounded above. Thus, the maximizer of the pseudo-likelihood function -- referred to as the pseudo-likelihood estimator -- always exists. In this article, we prove that the pseudo-likelihood estimator is strongly consistent.","short_abstract":"We consider a new method for estimating the parameters of univariate Gaussian mixture models. The method relies on a nonparametric density estimator $\\hat{f}_n$ (typically a kernel estimator). For every set of Gaussian mixture components, $\\hat{f}_n$ is used to find the best set of mixture weights. That set is obtained...","url_abs":"https://arxiv.org/abs/2510.14482","url_pdf":"https://arxiv.org/pdf/2510.14482v1","authors":"[\"Jüri Lember\",\"Raul Kangro\",\"Kristi Kuljus\"]","published":"2025-10-16T09:26:21Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}