An Empirical Comparison of EM Initialization Methods and Model Choice Criteria for Mixtures of Skew-Normal Distributions

We investigate, via simulation study, the performance of the EM algorithm for maximum likelihood estimation in finite mixtures of skew-normal distributions with component specific parameters. The study takes into account the initialization method, the number of iterations needed to attain a fixed stopping rule and the ability of some classical model choice criteria to estimate the correct number of mixture components. The results show that the algorithm produces quite reasonable estimates when using the method of moments to
obtain the starting points and that, combining them with the AIC, BIC, ICL or EDC criteria, represents a good alternative to estimate the number of components of the mixture. Exceptions occur in the estimation of the skewness parameters, notably when the sample size is relatively small, and in some classical problematic cases, as when the mixture components are poorly separated.
Key Words: EM algorithm; Skew-normal distribution; Finite mixture of distributions.