One and two sample Dvoretzky-Kiefer-Wolfowitz-Massart type inequalities for differing underlying distributions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913520360095744 |
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| author | Underwood, Nicolas G. Paillusson, Fabien |
| author_facet | Underwood, Nicolas G. Paillusson, Fabien |
| contents | Kolmogorov-Smirnov (KS) tests rely on the convergence to zero of the KS-distance $d(F_n,G)$ in the one sample case, and of $d(F_n,G_m)$ in the two sample case. In each case the assumption (the null hypothesis) is that $F=G$, and so $d(F,G)=0$. In this paper we extend the Dvoretzky-Kiefer-Wolfowitz-Massart inequality to also apply to cases where $F \neq G$, i.e. when it is possible that $d(F,G) > 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One and two sample Dvoretzky-Kiefer-Wolfowitz-Massart type inequalities for differing underlying distributions Underwood, Nicolas G. Paillusson, Fabien Statistics Theory Kolmogorov-Smirnov (KS) tests rely on the convergence to zero of the KS-distance $d(F_n,G)$ in the one sample case, and of $d(F_n,G_m)$ in the two sample case. In each case the assumption (the null hypothesis) is that $F=G$, and so $d(F,G)=0$. In this paper we extend the Dvoretzky-Kiefer-Wolfowitz-Massart inequality to also apply to cases where $F \neq G$, i.e. when it is possible that $d(F,G) > 0$. |
| title | One and two sample Dvoretzky-Kiefer-Wolfowitz-Massart type inequalities for differing underlying distributions |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2409.18087 |