{"ID":5552872,"CreatedAt":"2026-07-02T01:54:51.863792489Z","UpdatedAt":"2026-07-03T23:00:58.017711474Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.00261","arxiv_id":"2607.00261","title":"Worst-Case Maximal Inequalities for Heavy-tailed Random Vectors","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.","short_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...","url_abs":"https://arxiv.org/abs/2607.00261","url_pdf":"https://arxiv.org/pdf/2607.00261v1","authors":"[\"Woonyoung Chang\"]","published":"2026-06-30T23:13:13Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}