Testing homogeneity in contaminated mixture models

Contaminated mixture models (CMMs) have wide applications in the real world. Testing homogeneity in CMMs is an important and fundamental problem. In this article, we develop an EM-test for homogeneity in the general framework of the CMM with unbounded likelihood. The null limiting distribution of the test is shown to be a shifted mixture of chi-square distributions. Simulation studies demonstrate that the EM-test has excellent finite-sample performance. Two real-data examples illustrate the applications of the proposed method.