Jackknife empirical likelihood for the mean difference of two zero-inflated skewed populations

Abstract

In constructing a confidence interval for the mean difference of two independent populations, we may encounter the problem of having a low coverage probability when there are many zeros in the data, and the non-zero values are highly positively skewed. The violation of the normality assumption makes parametric methods inefficient in such cases. In this paper, jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) methods are proposed to construct a nonparametric confidence interval for the mean difference of two independent zero-inflated skewed populations. The JEL and AJEL confidence intervals are compared with the confidence intervals by normal approximation and empirical likelihood proposed by Zhou and Zhou (2005). Simulation studies are performed to assess the new methods. Two real-life datasets are also used as an illustration of the proposed methodologies.