论文标题
快速计算单方面Kolmogorov-Smirnov类型统计的P值
Fast calculation of p-values for one-sided Kolmogorov-Smirnov type statistics
论文作者
论文摘要
提出了一种用于计算Kolmogorov-Smirnov家族单方面统计精确p值的新方法。它涵盖了更高的批评统计数据，单方面加权的Kolmogorov-Smirnov统计数据以及单方面的Berk-Jones统计数据。除p值外，该方法还可以用于功率分析，查找α级阈值以及为经验分布函数的置信带的构建。 凭借其二次运行时和数值稳定性，该方法可以轻松地缩放到成千上万的样本大小，并且在样本量为25,000的样本量上运行少于一秒钟。这允许从事大型数据集的从业者使用精确的有限样本计算而不是近似方案。 该方法是基于纯跳转随机过程的边界划线概率的降低。然后，使用两种不同尺寸的FFT卷积来有效地传播非交叉路径的概率。该方法还具有统计数据以外的应用程序，例如在财务风险建模中。
A novel method for computing exact p-values of one-sided statistics from the Kolmogorov-Smirnov family is presented. It covers the Higher Criticism statistic, one-sided weighted Kolmogorov-Smirnov statistics, and the one-sided Berk-Jones statistics. In addition to p-values, the method can also be used for power analysis, finding alpha-level thresholds, and the construction of confidence bands for the empirical distribution function. With its quadratic runtime and numerical stability, the method easily scales to sample sizes in the hundreds of thousands and takes less than a second to run on a sample size of 25,000. This allows practitioners working on large data sets to use exact finite-sample computations instead of approximation schemes. The method is based on a reduction to the boundary-crossing probability of a pure jump stochastic process. FFT convolutions of two different sizes are then used to efficiently propagate the probabilities of the non-crossing paths. This approach has applications beyond statistics, for example in financial risk modeling.
