Statistical test for high order stochastic dominance under the density ratio model

In economics, medicine and other fields, how to compare the dominance relations between two distributions has been widely discussed. Usually population means or medians are compared. However, the population with a higher mean may not be what we will choose, since it may also have a larger variance. Stochastic dominance proposes a good solution to this problem. Subsequently, how to test stochastic dominance relations between two distributions is worth discussing. In this paper, we develop the test statistic of high order stochastic dominance under the density ratio model. In addition, we provide the asymptotic properties of test statistic and use the bootstrap method to obtain p-values to make decisions. Furthermore, the simulation results show that the proposed test statistics have the high test power.