Uniform Rates of Convergence of Some Representations of Extremes : a first approach

TL;DR

This paper establishes universal uniform convergence rates for asymptotic representations of sample extremes, providing bounds that are independent of the extreme value index, with plans for extension to broader cases.

Contribution

It introduces universal bounds for convergence rates of sample extremes that do not depend on the extreme value index, advancing theoretical understanding.

Findings

Provided universal convergence bounds for sample extremes

Bounds are independent of the extreme value index

Lays groundwork for extending to arbitrary sample extremes

Abstract

Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples extremes in coming papers.