Convergence in distribution of the P-P process in $L^1[0,1]$
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914507287166976 |
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| author | Beare, Brendan K. Kaji, Tetsuya |
| author_facet | Beare, Brendan K. Kaji, Tetsuya |
| contents | We show that the percentile-percentile (P-P) process constructed from an independent and identically distributed sample of pairs converges in distribution in $L^1[0,1]$ if and only if the associated P-P curve is absolutely continuous. When this condition holds, the limiting distribution is Gaussian and the process admits a valid bootstrap approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18390 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence in distribution of the P-P process in $L^1[0,1]$ Beare, Brendan K. Kaji, Tetsuya Probability Statistics Theory 62G30, 62E20 We show that the percentile-percentile (P-P) process constructed from an independent and identically distributed sample of pairs converges in distribution in $L^1[0,1]$ if and only if the associated P-P curve is absolutely continuous. When this condition holds, the limiting distribution is Gaussian and the process admits a valid bootstrap approximation. |
| title | Convergence in distribution of the P-P process in $L^1[0,1]$ |
| topic | Probability Statistics Theory 62G30, 62E20 |
| url | https://arxiv.org/abs/2601.18390 |