Robust estimation of mixture complexity for count data

For finite mixtures, consistent estimation of unknown number of components, called mixture complexity, is considered based on a random sample of counts, when the exact form of component probability mass functions are unknown but are postulated to belong to some parametric family. Following a recent approach of Woo and Sriram [2006. Robust estimation of mixture complexity. J. Amer. Statist. Assoc., to appear.], we develop an estimator of mixture complexity as a by-product of minimizing a Hellinger information criterion, when all the parameters associated with the mixture model are unknown. The estimator is shown to be consistent. Monte Carlo simulations illustrate the ability of our estimator to correctly determine the mixture complexity when the postulated Poisson mixture model is correct. When the postulated model is a Poisson mixture but the data comes from a negative binomial mixture with moderate to more extreme overdispersion in one of its components, simulation results show that our estimator continues to perform well. These confirm the efficiency of the estimator when the model is correctly specified and the robustness when the model is incorrectly specified. A count dataset with overdispersion and possible zero inflation is analyzed to further illustrate the ability of our estimator to determine the number of components.