Generalized fiducial confidence intervals for extremes |
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Authors: | Damian V Wandler Jan Hannig |
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Institution: | (1) The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA;(2) Colorado State University, Fort Collins, CO, USA;(3) The University of California at Davis, Davis, CA, USA; |
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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 . |
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Keywords: | |
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