Modified Likelihood Ratio Test for Finite Mixture Models

Abstract

Finite mixture models have wide applications. In genetics, a disease population might be a mixture of two subpopulations: one group of patients with genetic deficiency, and the other group without genetic deficiency. In fishery, a school of fish is a mixture of several age groups. One of the statistical problems is to make inference on the number of subpopulations based on data collected in these applications. Due to the irregularity of mixture models, classical methods, such as likelihood ratio test, are often hard to implement. In this talk, I shall give a brief discussion on most recent research results on this respect. The focus of the talk will be on the motivation and the use of modified likelihood ratio test. I shall explain the techniques involved in deriving the limiting distribution of the proposed test statistic. Simulation results will illustrate the closeness of the limit distribution to the finite sample one. The method is applied to a famous genetic data set to demonstrate the usefulness of the new method.