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.
Strong convergence of peaks over a threshold
Rizzelli, Stefano
2023
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.File in questo prodotto:
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