Some robust methods using empirical likelihood for two samples

In this paper we make some review of the empirical likelihood method for the two-sample case in a general framework. Empirical likelihood has several appealing properties: it is a nonparametric procedure, the shape of the respective confidence intervals or regions is data-driven and asymmetric, usually it admits the Bartlett correction. Regarding robust statistical inference we introduce the empirical likelihood method for the difference of smooth Huber estimators and trimmed means. Finally, we analyze the empirical level of the tests by some small simulation study.