Author:
Padoan Simone A.,Rizzelli Stefano
Abstract
Abstract
Extreme value theory plays an important role in providing approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the generalised Pareto distribution
$H_\gamma(x)$
as an approximation of the distribution
$F_t(s(t)x)$
of the excesses over a threshold t, where s(t) is a suitable norming function. We study the rate of convergence of
$F_t(s(t)\cdot)$
to
$H_\gamma$
in variational and Hellinger distances and translate it into that regarding the Kullback–Leibler divergence between the respective densities.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability