介于bootstrap方法在理论和实践的优势，其在统计的众多领域有着广泛的应用。在抽样调查领域，尽管学者们对bootstrap方法做了深入详实的研究，但其成果主要是基于简单随机抽样或分层随机抽样，且很多研究成果仅适用于方差估计。因此，研究bootstrap方法在复杂抽样下的理论性质就成为了一个迫切需要解决的前沿课题。本项目拟围绕bootstrap方法在复杂抽样下的统计推断展开。针对泊松抽样、简单随机抽样以及概率比例规模抽样，我们拟提出统一的bootstrap方法，并基于渐近枢轴量探究其二阶准确性。随后，我们将所提出的方法推广到假设检验问题中，以改进现有的检验方法。此外，针对每层一个点抽样法，我们提出基于bootstrap的方差估计，并在理论上探究所提出方法的可行性。本项目的实施有望丰富bootstrap方法在复杂抽样下的理论研究，提高复杂抽样下的统计推断的准确性。

Due to its theoretical and application advantage, bootstrap is widely used in statistics. In survey sampling, however, most bootstrap methods are proposed under simple random sampling or stratified random sampling and aim at variance estimation. In this project, we focus on statistical inference using bootstrap under complex sampling. We propose a unified bootstrap method for some commonly used complex sampling designs, including Poisson sampling, simple random sampling and probability-proportional-to-size sampling. The second-order accuracy of the proposed bootstrap method is investigated based on an asymptotic pivotal statistic. Then, we extend the proposed bootstrap method to hypothesis testing problems. We also consider a one-per-stratum sampling design and a bootstrap method for the variance estimation, and the corresponding theoretical properties are investigated. The implementation of this project will enrich the theoretical results of bootstrap methods and improve the accuracy of statistical inference under complex sampling.