Developing statistical procedures to determine the number of components, known as the mixture complexity, in finite mixture models remains an area of intense research. In many applications, it is important to find the mixture with fewest components that provides a satisfactory fit to the data. This article focuses on consistent estimation of unknown number of components in finite mixture models, when the exact form of the component densities are unknown but are postulated to be close to members of some parametric family. Minimum Hellinger distances are used to develop a robust estimator of mixture complexity, when all the parameters associated with the model are unknown. The estimator is shown to be consistent. When there is no contamination, Monte Carlo simulations for a wide variety of target mixtures illustrate the implementation and performance of the estimator. Robustness of the estimator examined via mixture contamination shows that, in contrast to an estimator based on Kullback-Leibler distance, the performance is unaffected by contamination. An example concerning hypertension is revisited to further illustrate the performance of the estimator.
Robust Estimation of Mixture Complexity