Variance-reduced sampling importance resampling

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.