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Confidence Intervals and Accuracy Estimation for Heavytailed Generalised Pareto Distribution (1996)
| Citations: | 6 - 2 self |
BibTeX
@TECHREPORT{Tajvidi96confidenceintervals,
author = {Nader Tajvidi},
title = {Confidence Intervals and Accuracy Estimation for Heavytailed Generalised Pareto Distribution},
institution = {},
year = {1996}
}
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Abstract
A rather recent approach for modelling extreme events is the so called peak over threshold (POT) method. The generalised Pareto distribution (GPD) is a twoparameter family of distributions which can be used to model exceedances over a threshold. We compare the empirical coverage of standard bootstrap and likelihood based confidence intervals for these parameters. Simulation results indicate that none of the methods give satisfactory intervals for small sample sizes. By applying a general method of D. N. Lawley, small sample correction factors for likelihood ratio statistics of parameters and quantiles of the GPD have been calculated. In many applications, lower limited condence interval for the shape parameter and upper limited confidence interval for the scale parameter of the GPD are of main interest. Simulations show that for sample sizes larger than 30 such intervals can be best constructed by incorporating the computed correction factors to the likelihood-based confidence intervals. While corrected likelihood method has better empirical coverage probability, the mean length of produced intervals are not longer than corresponding bootstrap confidence intervals. This article also investigates the performance of some bootstrap methods for estimation of accuracy measures of maximum likelihood estimators of parameters and quantiles of the GPD.
Keyphrases
confidence interval pareto distribution accuracy estimation bootstrap method sample size many application likelihood-based confidence interval satisfactory interval extreme event called peak standard bootstrap bootstrap confidence interval twoparameter family empirical coverage generalised pareto distribution small sample correction factor accuracy measure upper limited confidence interval general method recent approach shape parameter empirical coverage probability main interest likelihood ratio statistic mean length scale parameter simulation result limited condence interval maximum likelihood estimator small sample size likelihood method computed correction factor
