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 TopoTests. The presented tests work for samples in 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.

翻译：本文采用计算拓扑学工具——样本的欧拉特征曲线（ECC），进行单样本和双样本拟合优度检验，我们称之为TopoTests。所提出的检验方法适用于任意维度的样本，在一维情形下具有与当前最优方法相当的检验效力。研究表明，TopoTests的第一类错误可控，且第二类错误随样本量增大呈指数级衰减。通过大量数值模拟实验，我们验证了TopoTests的有效性。