Generalized likelihood‐ratio test of the number of components in finite mixture models
Jiahua Chen · Canadian Journal of Statistics · 1994
Abstract The number of components is an important feature in finite mixture models. Because of the irregularity of the parameter space, the log‐likelihood‐ratio statistic does not have a chi‐square limit distribution. It is very difficult to find a test with a specified significance level, and this is especially true for testing k — 1 versus k components. Most of the existing work has concentrated on finding a comparable approximation to the limit distribution of the log‐likelihood‐ratio statistic. In this paper, we use a statistic similar to the usual log likelihood ratio, but its null distribution is asymptotically normal. A simulation study indicates that the method has good power at detecting extra components. We also discuss how to improve the power of the test, and some simulations are performed.