This paper adopts a tool from computational topology, the Euler characteristic curve (ECC) of a sample, to perform one- and two-sample goodness of fit tests. We call our procedure TopoTests. The presented tests work for samples of arbitrary dimension, having comparable power to the state-of-the-art tests in the one-dimensional case. It is demonstrated that the type I error of TopoTests can be controlled and their type II error vanishes exponentially with increasing sample size. Extensive numerical simulations of TopoTests are conducted to demonstrate their power for samples of various sizes.

翻译：本文采用计算拓扑学工具——样本的欧拉示性数曲线（ECC），进行单样本和双样本拟合优度检验。我们将此方法命名为TopoTests。所提出的检验适用于任意维度的样本，在一维情况下具有与最新检验方法相当的功效。研究表明，TopoTests的第一类错误可被控制，且其第二类错误随样本量增加呈指数级衰减。通过大量数值模拟，我们验证了TopoTests在不同规模样本中的检验功效。