Multi-sample test based on bootstrap methods for second order stochastic dominance

Abstract

Statistical inferences under second order stochastic dominance for two sample case has a long and rich history. But the k(≥ 2) sample case has not been well studied. In this article we consider k(≥ 2) sample test for the equality of distribution functions against second order stochastic dominance alternative. A test statistic is constructed with isotonic regression estimates of stop-loss transform functions, and the asymptotic distribution of the proposed test is given. A bootstrap procedure is employed to obtain the p-value of the test, and some simulation results are presented to illustrate the proposed test method.