We introduce a novel approach called the Bayesian Jackknife empirical likelihood method for analyzing survey data obtained from various unequal probability sampling designs. This method is particularly applicable to parameters described by U-statistics. Theoretical proofs establish that under a non-informative prior, the Bayesian Jackknife pseudo-empirical likelihood ratio statistic converges asymptotically to a normal distribution. This statistic can be effectively employed to construct confidence intervals for complex survey samples. In this paper, we investigate various scenarios, including the presence or absence of auxiliary information and the use of design weights or calibration weights. We conduct numerical studies to assess the performance of the Bayesian Jackknife pseudo-empirical likelihood ratio confidence intervals, focusing on coverage probability and tail error rates. Our findings demonstrate that the proposed methods outperform those based solely on the jackknife pseudo-empirical likelihood, addressing its limitations.

翻译：我们提出一种名为贝叶斯折刀经验似然的新方法，用于分析通过多种不等概率抽样设计获得的调查数据。该方法特别适用于由U统计量描述的参数。理论证明表明，在无信息先验条件下，贝叶斯折刀伪经验似然比统计量渐近收敛于正态分布。该统计量可有效用于构建复杂调查样本的置信区间。本文研究了多种情形，包括辅助信息存在与否、设计权重或校准权重的使用。我们通过数值研究评估了贝叶斯折刀伪经验似然比置信区间的性能，重点考察了覆盖概率和尾部误差率。研究结果表明，所提方法优于仅基于折刀伪经验似然的方法，并弥补了后者的局限性。