- Published 2015 in Statistics and Computing

The maximum likelihood estimation in the finite mixture of distributions setting is an ill-posed problem that is treatable, in practice, through the EM algorithm. However, the existence of spurious solutions (singularities and non-interesting local maximizers) makes difficult to find sensible mixture fits for non-expert practitioners. In this work, a constrained mixture fitting approach is presented with the aim of overcoming the troubles introduced by spurious solutions. Sound mathematical support is provided and, which is more relevant in practice, a feasible algorithm is also given. This algorithm allows for monitoring solutions in terms of the constant involved in the restrictions, which yields a natural way to discard spurious solutions and a valuable tool for data analysts.

@article{GarcaEscudero2015AvoidingSL,
title={Avoiding spurious local maximizers in mixture modeling},
author={Luis Angel Garc{\'i}a-Escudero and Alfonso Gordaliza and Carlos Matr{\'a}n and Agust{\'i}n Mayo-Iscar},
journal={Statistics and Computing},
year={2015},
volume={25},
pages={619-633}
}