Using an inequality constraint to increase the power of the homogeneity tests for a two-sample problem with a mixture structure

Abstract

In recent years, two-sample testing problems with one sample from a mixture distribution have been studied in the literature. Some of these studies ignore an auxiliary information that the exposure or treatment involved in the two-sample problems may have a positive (or negative) effect on the response variable if the effect exists. The positive (or negative) effect implies an inequality constraint. In this paper, we establish the homogeneity tests for the two-sample problem with a mixture structure by considering the inequality constraint, and their null limiting distributions are shown to be a mixture of chi-square distributions. Simulation studies and real data analysis show that the proposed tests have better performance than the existing methods.