Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909326540537856 |
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| author | Dłotko, Paweł Hellmer, Niklas Stettner, Łukasz Topolnicki, Rafał |
| author_facet | Dłotko, Paweł Hellmer, Niklas Stettner, Łukasz Topolnicki, Rafał |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_14965 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions Dłotko, Paweł Hellmer, Niklas Stettner, Łukasz Topolnicki, Rafał Methodology Statistics Theory 62G10, 62R40 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. |
| title | Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions |
| topic | Methodology Statistics Theory 62G10, 62R40 |
| url | https://arxiv.org/abs/2210.14965 |