Wallot Sebastian, Leonardi Giuseppe
Max Planck Institute for Empirical Aesthetics, Grüneburgweg 14, 60322 Frankfurt am Main, Germany.
Faculty of Psychology, University of Finance and Management, ul. Pawia 55, 01-030 Warsaw, Poland.
Chaos. 2018 Aug;28(8):085712. doi: 10.1063/1.5024915.
Recurrence plots (RPs) have proved to be a very versatile tool to analyze temporal dynamics of time series data. However, it has also been conjectured that RPs can be used to model samples of random variables, that is, data that do not contain any temporal dependencies. In the current paper, we show that RPs can indeed be used to mimic nonparametric inferential statistics. Particularly, we use the case of the two-sample Kolmogorov-Smirnov test as a proof-of-concept, showing how such a test can be done based on RPs. Simulations on differences in mean, variance, and shape of two distributions show that the results of the classical two-sample Kolmogorov-Smirnov test and the recurrence-based test for differences in distributions of two independent samples scale well with each other. While the Kolmogorov-Smirnov test seems to be more sensitive in detecting differences in means, the recurrence based test seems to be more sensitive to detect heteroscedasticity and asymmetry. Potential improvements of our approach as well as extensions to tests with individual distributions are discussed.
递归图（RPs）已被证明是分析时间序列数据时间动态的一种非常通用的工具。然而，也有人推测递归图可用于对随机变量样本进行建模，即不包含任何时间依赖性的数据。在本文中，我们表明递归图确实可用于模拟非参数推断统计。特别是，我们以两样本柯尔莫哥洛夫-斯米尔诺夫检验为例进行概念验证，展示如何基于递归图进行此类检验。对两个分布的均值、方差和形状差异的模拟表明，经典的两样本柯尔莫哥洛夫-斯米尔诺夫检验结果与基于递归的两个独立样本分布差异检验结果相互之间具有良好的一致性。虽然柯尔莫哥洛夫-斯米尔诺夫检验在检测均值差异方面似乎更敏感，但基于递归的检验在检测异方差性和不对称性方面似乎更敏感。我们还讨论了该方法的潜在改进以及对单个分布检验的扩展。
