The primary objective of Extreme Value Theory is to estimate the probability of events occurring beyond the range of available data. Several parameters are of particular interest, including the extreme value index, \(\xi \) , which is associated with the tail weight of the distribution. It is the basis for estimating other parameters of extreme events, such as high quantiles. In dependent situations, which are very common in practice, another parameter emerges and can influence the estimation of high quantiles. This parameter is the extremal index, \(\theta \) , which is roughly defined as the reciprocal of the mean duration of values above a high level. A concise overview of several estimators for \(\theta \) is presented and the impact of its estimation for the estimation of high quantiles is shown. Given the challenges associated with semiparametric estimators, resampling methods will also be taken into account in a brief simulation and a real case study.

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Revisiting Estimation Methods for Some Parameters of Rare Events

  • Dora Prata Gomes,
  • Manuela Neves

摘要

The primary objective of Extreme Value Theory is to estimate the probability of events occurring beyond the range of available data. Several parameters are of particular interest, including the extreme value index, \(\xi \) , which is associated with the tail weight of the distribution. It is the basis for estimating other parameters of extreme events, such as high quantiles. In dependent situations, which are very common in practice, another parameter emerges and can influence the estimation of high quantiles. This parameter is the extremal index, \(\theta \) , which is roughly defined as the reciprocal of the mean duration of values above a high level. A concise overview of several estimators for \(\theta \) is presented and the impact of its estimation for the estimation of high quantiles is shown. Given the challenges associated with semiparametric estimators, resampling methods will also be taken into account in a brief simulation and a real case study.