Improving the power for testing against uniform stochastic ordering
Dewei Wang，(University of South Carolina)
2018.06.26, 9:30-10:30, N109
【Abstract】When comparing two continuous distributions F and G with respect to the uniform stochastic order, a convenient graphical tool is the ordinal dominance curve (ODC). If the ODC is star-shaped, then F and G are uniformly stochastically ordered. Motivated by this fact, a goodness-of-fit test of uniform stochastic ordering was proposed in Tang, Wang, and Tebbs (2017, Annals of Statistics), the test statistic of which depends on the Lp distance between an empirical estimator of the ODC and the estimator's least star-shaped majorant. To well control the probability of type I error, a unique least favorable configuration was found and used to determine fixed critical values. Though using fixed critical values yields a consistent test, it could severely weaken the power against alternatives that are nearby nulls other than the least favorable configuration. In this talk, a new method will be introduced to compute sample-based critical values, which facilitate significant improvements to the power of the test. Simulations and real data analysis are conducted to illustrate the advantages of the new method.