Application Of EM-test In The Homogeneity Test Of A Two-sample Problem

We consider a particular two-samples homogeneity testing problem which is often encountered to detect a treatment effect when some subjects in case-group are not af-fected by treatment because of the natural drug resistance in biological experiments and clinical efficacy tests.It's proved that differential variability as a criterion for selecting DNA methylation characteristics,can be more reliable than the mean difference in the identification of cancer risk markers,especially in the genomic methylation problem.In view of the importance of differential variability to homogeneity testing,we consider to propose a test which is designed to detect differential variability to solve this problem.We construct the penalized likelihood function in order to solve the infinity of likeli-hood function in traditional,and then propose an EM-test which is aimed at this homo-geneity testing from the general location-scale families in the two samples.We show that the EM-test statistic has a chi-square null limiting distribution.The asymptotic proper-ties of the EM-test under local alternatives are investigated,and sample size calculation is also discussed.For the integrality of the study,we also construct the similar theory in the test of mean difference.Simulation results show that the EM-test possesses more accurate empirical type I error and higher power than the existing methods.Finally,the real data examples are given to illustrate the application of the proposed method.