Bayesian jackknife empirical likelihood with complex surveys

This paper focuses on the application of the Bayesian jackknife empirical likelihood method to survey data collected from general single-stage unequal probability sampling and stratified sampling designs. We examine parameters characterized by U-statistics and establish the regularity conditions under which the posterior distribution, derived from the Bayesian jackknife pseudo-empirical likelihood under different priors, converges asymptotically to a normal distribution. We also investigate the impact of incorporating auxiliary information, as well as the use of design weights and calibration weights. Through simulations and real data analysis, we evaluate the effectiveness of the Bayesian jackknife pseudo-empirical likelihood credible intervals. Our results demonstrate that the proposed methodology not only offers significant advantages over methods that ignore the sampling design but also outperforms jackknife pseudo-empirical likelihood approaches.