A necessary and sufficient condition for convergence in distribution of the quantile process in $L^1(0,1)$
Statistics Theory
2026-04-17 v4 Statistics Theory
Abstract
We establish a necessary and sufficient condition for the quantile process based on iid sampling to converge in distribution in . The condition is that the quantile function is locally absolutely continuous and satisfies a slight strengthening of square integrability. If the quantile process converges in distribution then it may be approximated using the bootstrap.
Cite
@article{arxiv.2502.01254,
title = {A necessary and sufficient condition for convergence in distribution of the quantile process in $L^1(0,1)$},
author = {Brendan K. Beare and Tetsuya Kaji},
journal= {arXiv preprint arXiv:2502.01254},
year = {2026}
}
Comments
22 pages