用局部枢纽法提升精度：一种通用方差缩减方法
Enhancing Precision with the Local Pivotal Method: A General Variance Reduction Approach
AI总结：
本研究将原本用于离散总体抽样的局部枢纽法（LPM）拓展至任意连续分布场景，通过自动分层实现通用方差缩减，验证了其在多领域的有效性，还展示了其与其他方差缩减技术的结合效果，并提供了MATLAB和R的快速入门代码指南。
摘要：
局部枢纽法（LPM）是一种用于从离散总体中抽取分布均匀样本的成熟抽样方法。本研究展示了如何利用LPM从任意连续分布中抽样，从而在通用场景下实现强效的方差缩减。该方法可对任意维度的任意连续分布构建“自动分层”，并选取“精简”的分布均匀样本。我们通过多个示例验证了LPM的简洁性、通用性与有效性，示例涵盖积分的蒙特卡洛估计、期权定价以及非线性动力系统的稳定性估计。此外，我们还展示了LPM可与重要性抽样等其他方差缩减技术结合，以实现更优的方差缩减效果。为方便LPM的落地应用，我们提供了在MATLAB和R中使用LPM的快速入门指南，其中包含示例代码，演示仅需少量代码即可实现方差缩减。
英文摘要：
The local pivotal method (LPM) is a successful sampling method for taking well-spread samples from discrete populations. We show how the LPM can be utilized to sample from arbitrary continuous distributions and thereby give powerful variance reduction in general cases. The method creates an ``automatic stratification" on any continuous distribution, of any dimension, and selects a ``thin" well-spread sample. We demonstrate the simplicity, generality and effectiveness of the LPM with various examples, including Monte Carlo estimation of integrals, option pricing and stability estimation in non-linear dynamical systems. Additionally, we show how the LPM can be combined with other variance reduction techniques, such as importance sampling, to achieve even greater variance reduction. To facilitate the implementation of the LPM, we provide a quick start guide to using LPM in MATLAB and R, which includes sample code demonstrating how to achieve variance reduction with just a few lines of code.
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