Empirical likelihood ratio under infinite second moment for two-sample problems

Abstract

In this article, the author focuses on the simple and yet very important case of making inference on the difference of two population means using the empirical likelihood approach. It is shown that the log empirical likelihood ratio statistic for the difference of two population means converges in distribution to as when the two population are in the domain of attraction of normal law but have infinite variances. The simulation results show that the empirical likelihood ratio method is applicable under the infinite second moment condition.