The sampling importance resampling method is widely utilized in various fields, such as numerical integration and statistical simulation. In this paper, two modified methods are presented by incorporating two variance reduction techniques commonly used in Monte Carlo simulation, namely antithetic sampling and Latin hypercube sampling, into the process of sampling importance resampling method respectively. Theoretical evidence is provided to demonstrate that the proposed methods significantly reduce estimation errors compared to the original approach. Furthermore, the effectiveness and advantages of the proposed methods are validated through both numerical studies and real data analysis.

翻译：采样重要性重采样方法被广泛应用于数值积分和统计模拟等多个领域。本文通过将蒙特卡洛模拟中常用的两种方差缩减技术——对偶采样和拉丁超立方采样——分别融入采样重要性重采样过程，提出了两种改进方法。理论分析表明，与原始方法相比，所提方法能显著降低估计误差。此外，通过数值研究和实际数据分析，验证了所提方法的有效性和优势。