Bayesian empirical likelihood inference for the mean absolute deviation

The mean absolute deviation (MAD) is a direct measure of the dispersion of a random variable about its mean. In this paper, the empirical likelihood (EL) and the adjusted EL methods for the MAD are proposed. The Bayesian empirical likelihood, the Bayesian adjusted empirical likelihood, the Bayesian jackknife empirical likelihood and the Bayesian adjusted jackknife empirical likelihood methods are used to construct credible intervals for the MAD. Simulation results show that the proposed EL method performs better than the JEL in Zhao et al. [Jackknife empirical likelihood inference for the mean absolute deviation. Comput Stat Data Anal. 2015;91:92-101], and the proper prior information improves coverage rates of confidence/credible intervals. Two real datasets are used to illustrate the new procedures.