Variance-reduced sampling importance resampling

TL;DR

This paper introduces two variance reduction techniques, antithetic sampling and Latin hypercube sampling, into sampling importance resampling to improve estimation accuracy, validated through theoretical analysis and empirical studies.

Contribution

It presents novel modifications of sampling importance resampling by integrating variance reduction methods, enhancing its efficiency and accuracy.

Findings

Significant reduction in estimation errors with proposed methods.

Theoretical proof of variance reduction effectiveness.

Empirical validation through numerical and real data analyses.

Abstract

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.