EM Test Under Inequality Constraints

We consider a particular two-sample homogeneity testing problem which often involves in detecting a treatment effect when not all experimental subjects respond to treatment due to drug resistance in efficay testing.Generally speaking,the sugjects in experimental group will be treated with target drug in order to study the efficacy of a certain drug.Therefore,the problem that how to test the two-sample homogeneity under the inequality constraints is discussed.We construct a penalized likelihood function for a general location-scale distribution family in terms of the problem that the likelihood function is unbounded and the Fisher information of the mixed ratio may be infinitely large.Considering the positive mean-shift information,we suggest an EM-test statistic based on the penalized likelihood function which is essential to homogeneity testing in the two samples.Follwing are the main contents: First of all,we study the theorey of EM-test under inequality constraints that ?2-?1? 0.It is proved that the EM-test statistic converges to limiting distribution1/2?2/1+1/2?2/2or1/2?2/0+1/2?2/1 when variances are not equal or equal.Next,simulation results for normal distribution and logistic distribution by software R show that our proposed EM test method has more accurate empirical type I error rate and higher power when compared with the existing methods.Finally,the example of micemorphine indicates the validity of our proposed method.