Improved Estimation of the Extreme Value Index Using Related Variables

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Abstract

Heavy tailed phenomena are naturally analyzed by extreme value statistics. A
crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We consider the situation where we have next to the n observations of interest another n+m observations of one or more related variables, like, e.g., financial losses due to earthquakes and the related amounts of energy released, for a
longer period than that of the losses. Based on such a data set, we present an adapted version of the Hill estimator that shows greatly improved behavior and we establish the asymptotic normality of this estimator. For this adaptation the tail dependence between the variable of interest and the related variable(s) plays an important role. A simulation study confirms the substantially improved performance of our adapted estimator relative to the Hill estimator. We also present an application to the aforementioned earthquake losses.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages16
Volume2018-025
Publication statusPublished - 16 Jul 2018

Publication series

NameCentER Discussion Paper
Volume2018-025

Fingerprint

Extreme Value Index
Hill Estimator
Earthquake
Extreme Value Statistics
Tail Dependence
Estimator
Asymptotic Normality
Tail
Probability Distribution
Simulation Study
Energy
Observation

Keywords

  • asymptotic normality
  • heavy tail
  • Hill estimator
  • tail dependence
  • variance reduction

Cite this

Ahmed, H., & Einmahl, J. (2018). Improved Estimation of the Extreme Value Index Using Related Variables. (CentER Discussion Paper; Vol. 2018-025). Tilburg: CentER, Center for Economic Research.
Ahmed, Hanan ; Einmahl, John. / Improved Estimation of the Extreme Value Index Using Related Variables. Tilburg : CentER, Center for Economic Research, 2018. (CentER Discussion Paper).
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Ahmed, H & Einmahl, J 2018 'Improved Estimation of the Extreme Value Index Using Related Variables' CentER Discussion Paper, vol. 2018-025, CentER, Center for Economic Research, Tilburg.

Improved Estimation of the Extreme Value Index Using Related Variables. / Ahmed, Hanan; Einmahl, John.

Tilburg : CentER, Center for Economic Research, 2018. (CentER Discussion Paper; Vol. 2018-025).

Research output: Working paperDiscussion paperOther research output

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N2 - Heavy tailed phenomena are naturally analyzed by extreme value statistics. Acrucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We consider the situation where we have next to the n observations of interest another n+m observations of one or more related variables, like, e.g., financial losses due to earthquakes and the related amounts of energy released, for alonger period than that of the losses. Based on such a data set, we present an adapted version of the Hill estimator that shows greatly improved behavior and we establish the asymptotic normality of this estimator. For this adaptation the tail dependence between the variable of interest and the related variable(s) plays an important role. A simulation study confirms the substantially improved performance of our adapted estimator relative to the Hill estimator. We also present an application to the aforementioned earthquake losses.

AB - Heavy tailed phenomena are naturally analyzed by extreme value statistics. Acrucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We consider the situation where we have next to the n observations of interest another n+m observations of one or more related variables, like, e.g., financial losses due to earthquakes and the related amounts of energy released, for alonger period than that of the losses. Based on such a data set, we present an adapted version of the Hill estimator that shows greatly improved behavior and we establish the asymptotic normality of this estimator. For this adaptation the tail dependence between the variable of interest and the related variable(s) plays an important role. A simulation study confirms the substantially improved performance of our adapted estimator relative to the Hill estimator. We also present an application to the aforementioned earthquake losses.

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Ahmed H, Einmahl J. Improved Estimation of the Extreme Value Index Using Related Variables. Tilburg: CentER, Center for Economic Research. 2018 Jul 16. (CentER Discussion Paper).