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

Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions