Rates of convergence for Renyi entropy in extreme value theory

TL;DR

This paper investigates how quickly the Renyi entropy of normalized maxima converges to that of max stable laws in extreme value theory, providing insights into the rate of this convergence.

Contribution

It extends previous work by establishing the rate of convergence of Renyi entropy for linearly normalized partial maxima in extreme value theory.

Findings

Derived explicit convergence rates for Renyi entropy

Generalized previous convergence results to broader conditions

Enhanced understanding of entropy behavior in extreme value limits

Abstract

Max stable laws are limit laws of linearly normalized partial maxima of independent identically distributed random variables. Saeb (2014) proves that the Renyi entropy of order b (b > 1) of linear normalized maximum of iid random variables with continuous differentiable density is convergent to the Renyi entropy of order b of the max stable laws. In this paper, we study the rate of convergence result for Renyi entropy for linearly normalized partial maxima.