AI 中文总结
针对非参数置换检验中精确计算p值的难题，提出哈希增强自适应多级分裂蒙特卡罗算法，以Kolmogorov-Smirnov和Mann-Whitney U检验为例展示其应用，通过与精确算法比较证明准确性，还提供Python包实现对用户定义统计量的p值估计。
AI 中文摘要
非参数置换检验在统计分析中广泛应用。然而，精确计算检验p值在算法上具有挑战性，特别是对于具有复杂检验统计量的自定义检验。相比之下，蒙特卡罗抽样可轻松应用于任何检验统计量，但估计小p值时相对准确性较差。本文提出了一种哈希增强自适应多级分裂蒙特卡罗算法，能在两样本置换检验中精确估计任意小的p值。以Kolmogorov-Smirnov和Mann-Whitney U检验为例，强调与检验统计量分布离散性相关的潜在陷阱及解决方法。通过与精确算法比较，证明了所提算法提供的p值估计的准确性及相关置信区间的有效性。还在Python包hamstest中提供了该算法的参考实现，可对用户定义的统计量进行p值估计。
英文摘要
Nonparametric permutation tests are widely used for statistical analysis. However, exact computation of test p-values can be algorithmically challenging, particularly for custom tests with complex test statistics. In contrast, Monte Carlo sampling can be easily applied to any test statistic, but it suffers from poor relative accuracy when estimating small p-values, interfering with multiple hypothesis testing correction and leading to other issues. In this work, we present a hash-augmented adaptive multilevel splitting Monte Carlo algorithm that enables accurate estimation of arbitrarily small p-values in two-sample permutation tests. Using the Kolmogorov-Smirnov and the Mann-Whitney U tests as examples, we highlight potential pitfalls related to the discreteness of the test statistic distribution and show how to address them. By comparing with an exact algorithm, we demonstrate the accuracy of the p-value estimates provided by the proposed algorithm and the validity of the associated confidence intervals. We provide a reference implementation of the proposed algorithm in the Python package hamstest, which allows p-value estimation for a user-defined statistic.
