Nonparametric density mixtures and smoothed penalized nonparametric likelihood: the match made in heaven

Music City Center 

One of the most important tools for exploring heterogeneous data in many application areas are finite density mixture models. Non- and semiparametric finite density mixture models are a relatively new field of research within a wider area of finite density mixture models that has a lot to offer in terms of theory, methodology, and applications. In this presentation, we discuss a general approach to designing algorithms for estimation of components of these models based on the nonparametric smoothed penalized maximum likelihood. This approach results in converging algorithms for many different semi- and nonparametric finite density mixture models, including the multivariate ones. In doing so, this approach unifies conceptually many seemingly disparate mixture models. We also illustrate the usefulness of the proposed approach by showing the large-sample consistency of the implicit estimator that results from applying this method. Several simulations and real-life applications round out our presentation.