2020/06/01 by Tudor Manole, Manole, Tudor, Nhat Ho +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST) #math.ST #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.2006.00704
Both authors contributed equally to this work
arxiv created 2020/06/01 · openalex publication_date 2020/06/01 · arxiv updated 2020/06/02 · openalex created_date 2020/06/05 · openalex updated_date 2026/07/28
We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of the mixture are known and fixed, but make no separation assumption on the underlying mixture components. A phase transition is shown to exist in the optimal parameter estimation rate, depending on whether or not the mixture is balanced. Key to our analysis is a careful study of the dependence between the parameters of location-scale Gaussian mixture models, as captured through systems of polynomial equalities and inequalities whose solution set drives the rates we obtain. A simulation study illustrates the theoretical findings of this work.