Worst-Case Maximal Inequalities for Heavy-tailed Random Vectors

Woonyoung Chang

Worst-Case Maximal Inequalities for Heavy-tailed Random Vectors

Statistics Theory 2026-06-30 v1

Authors: Woonyoung Chang

Abstract

This paper establishes finite-sample worst-case maximal inequalities for averages of independent centered heavy-tailed random vectors. The object of interest is the expected top- $k$ Euclidean norm of the sample average, which includes the expected coordinate-wise maximum as the special case $k=1$ . Under coordinatewise variance constraints and tail-envelope constraints, the worst-case value is characterized up to universal constants over the class of distributions satisfying a finite $q$ :th envelope moment condition. Analogous bounds are obtained for the sub-Weibull envelope class and the marginal sub-Weibull class.

Cite

@article{arxiv.2607.00261,
  title  = {Worst-Case Maximal Inequalities for Heavy-tailed Random Vectors},
  author = {Woonyoung Chang},
  journal= {arXiv preprint arXiv:2607.00261},
  year   = {2026}
}