On a closer look at weighted likelihood in the context of mixtures

The performance of the weighted likelihood methodology in the context of mixtures is studied in detail. Specifically, we study the behavior of the method under two types of misspecification. Those are (1) probability model misspecification, which refers to both, component misspecification and probability distribution misspecification, and (2) variance structure misspecification. We contrast the behavior of the weighted likelihood estimates with that of Huber-type M-estimates and maximum likelihood estimates. We present simulation results which exemplify the role of the starting values in the convergence of the weighted likelihood algorithm. We then discuss the relationship of these results with the problem of model selection.