In scientific investigations, a population is often suspected of containing several more homogeneous sub-populations. Such a population structure is most accurately described by a finite mixture model but the model should only be adopted with a statistically significant evidence through a rigorous hypothesis test. Developing valid and effective statistical inference methods on mixing distribution is an important research topic yet it posts serious technical challenges. Classical procedures when applied to mixture models often have sophisticated asymptotic properties which render them useless in applications. For a large number of finite mixture models, we have successfully designed corresponding EM-tests whose limiting distributions are easier to derive mathematically, simple for implementation in data analysis.
In this talk, we will first give a general introduction to EM-test. We will illustrate their elegant asymptotic properties and present a new approach to the tuning of ancillary parameters. We will also present some results on the sample size determination.