Empirical likelihood estimation in multivariate mixture models with repeated measurements

Multivariate mixtures are encountered in situations where the data are repeated or clustered measurements in the presence of heterogeneity among the observations with unknown proportions. In such situations, the main interest may be not only in estimating the component parameters, but also in obtaining reliable estimates of the mixing proportions. In this paper, we propose an empirical likelihood approach combined with a novel dimension reduction procedure for estimating parameters of a two-component multivariate mixture model. The performance of the new method is compared to fully parametric as well as almost nonparametric methods used in the literature.