This article constructs a consistent robust estimator of mixture complexity 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 the approach of Woo and Sriram (2004), we develop a robust estimator of mixture complexity using Minimum Hellinger distances, when all the parameters associated with the mixture model are unknown. When there is no data contamination, Monte Carlo simulations for a wide variety of target Poisson mixtures, including Zero-inflated Poisson mixtures, illustrate the implementation and performance of the estimator. Robustness of the estimator examined via contaminated Poisson mixtures shows that the performance is unaffected by contamination. Two examples, one with zero-inflation, are used to further illustrate the performance of the estimator.
Robust Estimation of Number Components in Finite Mixture Models for Count Data