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.