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Convergence in distribution of the P-P process in $L^1[0,1]$

Probability 2026-04-28 v3 Statistics Theory Statistics Theory

Abstract

We show that the percentile-percentile (P-P) process constructed from an independent and identically distributed sample of pairs converges in distribution in L1[0,1]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.

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Cite

@article{arxiv.2601.18390,
  title  = {Convergence in distribution of the P-P process in $L^1[0,1]$},
  author = {Brendan K. Beare and Tetsuya Kaji},
  journal= {arXiv preprint arXiv:2601.18390},
  year   = {2026}
}

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7 pages