The sample fraction in peaks-over-threshold problems where the second-order expansion is valid with specific reference to the generalized Pareto distribution
Statistics Theory
2016-12-15 v1 Statistics Theory
Abstract
In samples from a heavy-tailed distribution a second-order approximation is often use to approximate the tail function. Based on the parameters of the approximation, an optimal sample fraction can be estimated which is then used to estimate the index. Given that the observations are above a threshold and has an approximate generalized Pareto distribution, an expression is derived for the percentile above which the second-order approximation is valid
Keywords
Cite
@article{arxiv.1612.04636,
title = {The sample fraction in peaks-over-threshold problems where the second-order expansion is valid with specific reference to the generalized Pareto distribution},
author = {J. Martin van Zyl},
journal= {arXiv preprint arXiv:1612.04636},
year = {2016}
}