Clustering with mixtures of log-concave distributions

The EM algorithm is a popular tool for clustering observations via a parametric mixture model. Two disadvantages of this approach are that its success depends on the appropriateness of the assumed parametric model, and that each model requires a different implementation of the EM algorithm based on model-specific theoretical derivations. We show how this algorithm can be extended to work with the flexible, nonparametric class of log-concave component distributions. The advantages of the resulting algorithm are: first, it is not restricted to parametric models, so it no longer requires to specify such a model and its results are no longer sensitive to a misspecification thereof. Second, only one implementation of the algorithm is necessary. Furthermore, simulation studies based on the normal mixture model show that there seems to be no noticeable performance penalty of this more general nonparametric algorithm vis-a-vis the parametric EM algorithm in the special case where the assumed parametric model is indeed correct.