Two-sample Density-based Empirical Likelihood Tests for Stochastically Ordered Alternatives

The empirical likelihood method based on the empirical distribution functions is a wellaccepted statistical tool for testing. Recently, the density-based empirical likelihood technique was proposed and applied successfully to construct a powerful two-sample nonparametric likelihood ratio test based on samples entropy. However, while the problem of one-sided alternatives has received considerable attention in the case of the likelihood ratio tests, the two-sample density-based empirical likelihood test was proposed only in the context of the two-sided alternative. Hence, it is not suitable for a variety of applied statistical problems where the one-sided test should be driven by the scientific question and the data analyzed. In this paper we show how one-sample density-based empirical likelihood tests can be constructed and provide a proof of their consistency. Monte Carlo simulations confirm that the proposed one-sided nonparametric tests have approximately same powers as that of the Wilcoxon test detecting a constant shift in the one-sided two-sample problem and are preferable to the Wilcoxon test detecting a nonconstant shift.