Hypothesis testing for finite mixture models

Hypothesis testing for finite mixture model has long been a challenging problem. The standard likelihood ratio test (LRT) does not have the usual asymptotic χ2 distribution partly because the mixture model is not identifiable under null hypothesis. A simple class of hypothesis test procedures for finite mixture models based on goodness of fit (GOF) test statistics is investigated. The suggested hypothesis test procedure is easy to understand and use and can be applied to many mixture models with continuous data. Five commonly used goodness of fit test statistics are considered and compared. The limit distribution of test statistics is simulated based on the bootstrap method. It is demonstrated that a simple application of GOF test statistics to finite mixture models can provide comparable or even superior hypothesis test performance compared to the existing cutting edge EM test method through extensive simulation studies. The effectiveness of GOF test to choose the number components is also demonstrated based on limited empirical studies and a real data application.