论文标题
部分可观测时空混沌系统的无模型预测
Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions
论文作者
论文摘要
本文采用了计算拓扑（样品的Euler特征曲线（ECC））的工具，以执行拟合测试的一个和两样本的优点。我们称我们的过程拓扑。提出的测试适用于任意维度的样品，在一维情况下具有可比的功率。证明可以控制TOPOTEST的I型误差，其II型错误随着样本量的增加而呈指数级消失。进行了拓扑兴奋的广泛数值模拟，以证明其对各种大小样品的功能。
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.
