Jackknife empirical likelihood inference for the mean absolute deviation

In statistics mean absolute deviation plays an important role in measuring spread of a data. In this paper, we focus on using the jackknife, the adjusted and the extended jackknife empirical likelihood methods to construct confidence intervals for the mean absolute deviation of a random variable. The empirical log-likelihood ratio statistic is derived whose asymptotic distribution is a standard chi-square distribution. The results of simulation study show the comparison of the average length and coverage probability by using jackknife empirical likelihood methods and normal approximation method. The proposed adjusted and extended jackknife empirical likelihood methods perform better than other methods, in particular for skewed distributions. We use real data sets to illustrate the proposed jackknife empirical likelihood methods.