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Extremes

, Volume 15, Issue 1, pp 67–87 | Cite as

Generalized fiducial confidence intervals for extremes

  • Damian V. WandlerEmail author
  • Jan Hannig
Article

Abstract

The generalized Pareto distribution is relevant to many situations when modeling extremes of random variables. In particular, peaks over threshold data approximately follow the generalized Pareto distribution. We use a fiducial framework to perform inference on the parameters and the extreme quantiles of the generalized Pareto. This inference technique is demonstrated both when the threshold is a known and unknown parameter. Assuming the threshold is a known parameter resulted in fiducial intervals with good empirical properties and asymptotically correct coverage. Likewise, our simulation results suggest that the fiducial intervals and point estimates compare favorably to the competing methods seen in the literature. The proposed intervals for the extreme quantiles when the threshold is unknown also have good empirical properties regardless of the underlying distribution of the data. Comparisons to a similar Bayesian method suggest that the fiducial intervals have better coverage and are similar in length with fewer assumptions. In addition to simulation results, the proposed method is applied to a data set from the NASDAQ 100. The data set is analyzed using the fiducial approach and its competitors for both cases when the threshold is known and unknown. R code for our procedure can be downloaded at http://www.unc.edu/~hannig/.

Keywords

Fiducial inference Extreme quantile Peaks over threshold MCMC 

AMS 2000 Subject Classifications

62G32 62G05 62F10 62P12 62P05 62P30 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of StatisticsColorado State UniversityFort CollinsUSA
  2. 2.Department of Statistics and Operations ResearchThe University of North Carolina at Chapel HillChapel HillUSA

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