Spurred by applications in genetics and other fields, research in finite mixture models has recently enjoyed an explosion of activity. One problem of practical interest is the determination of the number of components in the mixture distribution. This can be done using the generalized likelihood ratio test. However, it is known that the likelihood ratio test statistic may not have the typical chi-squared type null distribution and may even diverge under the null hypothesis of no mixture. The exact behavior of the corresponding likelihood ratio test statistic has long remained a mystery. The main objective of this talk is to give an overview of some recent advances in this field and to discuss some remaining challenges.
Group for Research in Decision Analysis