Consistent estimation of mixture complexity

Abstract

The consistent estimation of mixture complexity is of fundamental importance in many applications of finite mixture models. An enormous body of literature exists regarding the application, computational issues and theoretical aspects of mixture models when the number of components is known, but estimating the unknown number of components remains an area of intense research effort. This article presents a semiparametric methodology yielding almost sure convergence of the estimated number of components to the true but unknown number of components. The scope of application is vast, as mixture models are routinely employed across the entire diverse application range of statistics, including nearly all of the social and experimental sciences.