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 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.
Keywords
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}
}
Comments
7 pages