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

Brendan K. Beare; Tetsuya Kaji

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arXiv · 2601.18390

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

Brendan K. Beare·Tetsuya Kaji

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Abstract

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.

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Brendan K. Beare, Tetsuya Kaji. 2026-01-26. Convergence in distribution of the P-P process in $L^1[0,1]$. https://arxiv.org/abs/2601.18390

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