Abstract Details
Activity Number:
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643
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Type:
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Contributed
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Date/Time:
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Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Statistics and the Environment
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Abstract #311571
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View Presentation
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Title:
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Improved Small Sample Inference for the Generalized Pareto Distribution Through a Monte Carlo Adjustment to the Signed Root of the Log-Likelihood Ratio Statistic
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Author(s):
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David Smith*+
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Companies:
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Tennessee Tech University
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Keywords:
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Generalized Pareto distribution ;
inference ;
log-likelihood ratio statistic ;
confidence intervals ;
small samples
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Abstract:
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Estimation methods for the Generalized Pareto distribution have been well studied. While the maximum likelihood method may yield adequate results for cases in which the shape parameter falls between -.5 to 5 and large sample sizes, very little has been done for small sample sizes. Small sample sizes can occur when fitting the exceedance over a threshold. We study an adjustment which centers and scales the signed root of the log-likelihood ratio statistic. The Monte Carlo adjustment is easily derived and does not require complex calculations that are often required to condition on ancillary statistics. One-sided inference and confidence intervals for shape, scale, and m-year return levels are compared to profile likelihood and delta methods. Considerable improvement is shown for small samples and demonstrated with examples.
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Authors who are presenting talks have a * after their name.
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