In this article, we propose a one-sample test to check whether the support of the unknown distribution generating the data is homologically equivalent to the support of some specified distribution or not OR using the corresponding two-sample test, one can test whether the supports of two unknown distributions are homologically equivalent or not. In the course of this study, test statistics based on the Betti numbers are formulated, and the consistency of the tests is established under the critical and the supercritical regimes. Moreover, some simulation studies are conducted and results are compared with the existing methodologies such as Robinson's permutation test and test based on mean persistent landscape functions. Furthermore, the practicability of the tests is shown on two well-known real data sets also.
翻译:在本条中,我们建议进行一模一样的测试,以检查生成数据的未知分布支持是否与某些特定分布支持的同质等同,是否使用相应的两样的测试,人们可以测试两种未知分布的支撑是否等同,在本研究过程中,根据贝蒂数字编制测试统计数据,并在关键和超临界制度下确定测试的一致性,此外,还进行了一些模拟研究,并将结果与现有的方法进行比较,如罗宾逊的调整测试和基于平均持久性地貌功能的测试,此外,测试是否可行还体现在两个众所周知的真实数据集上。