Empirical likelihood-based confidence intervals for data with possible zero observations

In statistical applications, we often encounter a situation where a substantial number of observations takes zero value and at the same time the non-zero observations are highly skewed. We propose empirical likelihood-based non-parametric confidence intervals for the mean parameter which have two unique features. One is that the information contained in the zero observations is fully utilized. The other is that the proposed confidence intervals are more reflective to the skewness in the non-zero observations than those based on the asymptotic normality.