A comment on rates of convergence for density function in extreme value theory and Rényi entropy

Abstract

De Haan and Resnick [Ann. Probab. 10 (1982), no. 2, 396–413] have shown that the Rényi entropy of order β \beta ( β > 1 \beta >1 ) of normalized sample maximum of independent and identically distributed (iid) random variables with continuous differentiable density converges to the Rényi entropy of order β \beta of a max stable law. In this paper, we review the rate of convergence for density function in extreme value theory. Finally, we study the rate of convergence for Rényi entropy in the case of normalized sample maxima.