English

Improving discrepancy by moving a few points

Statistics Theory 2025-09-15 v2 Probability Statistics Theory

Abstract

We show how to improve the discrepancy of an iid sample by moving only a few points. Specifically, modifying O(m) O(m) sample points on average reduces the Kolmogorov-Smirnov distance to the population distribution to 1/m1/m.

Cite

@article{arxiv.2503.04100,
  title  = {Improving discrepancy by moving a few points},
  author = {Gleb Smirnov and Roman Vershynin},
  journal= {arXiv preprint arXiv:2503.04100},
  year   = {2025}
}

Comments

9 pages; accepted version

R2 v1 2026-06-28T22:08:42.471Z