For finite mixtures, consistent estimation of number of components, known as mixture complexity, is considered based on a random sample of counts distributed according to a probability mass function, whose exact form is unknown but is postulated to be close to members of some parametric family of finite mixtures. Following a recent approach of Woo and Sriram (2004), we develop a robust estimator of mixture complexity using Minimum Hellinger distance, when all the parameters associated with the mixture model are unknown. The estimator is shown to be consistent. Monte Carlo simulations are carried out to illustrate the ability of our estimator to correctly determine the mixture complexity when the postulated Poisson mixture models are correct. When the postulated Poisson mixture model is not strictly correct, that is when the samples come from a contaminated Poisson mixture, simulation results show that the performance of our estimator is unaffected by contamination. These confirm the efficiency of the estimator when the model is correctly specified and robustness when the model is incorrectly specified. Three count datasets with overdispersion, two of which with possible zero-inflation, are analyzed to further illustrate the ability of our estimator to determine the number of components.
Robust Estimation of Mixture Complexity for Count Data