Distribution-free two-sample testing with blurred total variation distance
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910119116144640 |
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| author | Hore, Rohan Barber, Rina Foygel |
| author_facet | Hore, Rohan Barber, Rina Foygel |
| contents | Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular, certifying equality of distributions, or even providing a tight upper bound on the total variation (TV) distance between the distributions, is impossible to achieve in a distribution-free regime. In this work, we examine the blurred TV distance, a relaxation of TV distance that enables us to perform inference without assumptions on the distributions. We provide theoretical guarantees for distribution-free upper and lower bounds on the blurred TV distance, and examine its properties in high dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05862 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distribution-free two-sample testing with blurred total variation distance Hore, Rohan Barber, Rina Foygel Machine Learning Statistics Theory Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular, certifying equality of distributions, or even providing a tight upper bound on the total variation (TV) distance between the distributions, is impossible to achieve in a distribution-free regime. In this work, we examine the blurred TV distance, a relaxation of TV distance that enables us to perform inference without assumptions on the distributions. We provide theoretical guarantees for distribution-free upper and lower bounds on the blurred TV distance, and examine its properties in high dimensions. |
| title | Distribution-free two-sample testing with blurred total variation distance |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2602.05862 |