Abstract: Empirical likelihood based tests for the presence of uniform stochastic ordering (or hazard rate ordering) among two univariate distributions functions (DFs) are developed when the data are right censored in the one- and two-sample cases. The proposed test statistics are formed by taking the supremum of some functional of localized empirical likelihood test statistics. The null asymptotic distributions of these test statistics are distribution-free and have simple representations in terms of a standard Brownian motion. Simulations show that the tests we propose outperform, in terms of power, the one sided log-rank test at many distributions. The stochastic ordering case is shown to be a special case of our procedure. We illustrate our theoretical results with an example.

Key words and phrases: Empirical likelihood, stochastic ordering, uniform stochastic ordering.