×

zbMATH — the first resource for mathematics

A simulation-based hyperparameter selection for quantile estimation of the generalized extreme value distribution. (English) Zbl 1077.62040
Summary: A systematic way of selecting hyperparameters of the prior on the shape parameter of the generalized extreme value distribution (GEVD) is presented. The optimal selection is based on a Monte Carlo simulation in the generalized maximum likelihood estimation (GMLE) framework. A scaled total misfit measure for the accurate estimation of upper quantiles is used for the selection criterion. The performance evaluations for GEVD and non-GEVD show that the GMLE with selected hyperparameters produces more accurate quantile estimates than the MLE, the L-moments estimator, and E. S. Martins and J. R. Stedinger’s GMLE [Water Resource Res. 36, 737–744 (2000)].

MSC:
62G32 Statistics of extreme values; tail inference
65C05 Monte Carlo methods
86A05 Hydrology, hydrography, oceanography
62E15 Exact distribution theory in statistics
62P12 Applications of statistics to environmental and related topics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Coles, S.; Dixon, M., Likelihood-based inference for extreme value models, Extremes, 2, 5-23, (1999) · Zbl 0938.62013
[2] Efron, B.; Tibshirani, R.J., An introduction to the bootstrap, (1993), Chapman & Hall/CRC Press Boca Raton · Zbl 0835.62038
[3] Hirose, H., Maximum likelihood parameter estimation by model augmentation with applications to the extended four-parameter generalized gamma distribution, Math. comp. simul., 54, 81-97, (2000)
[4] Hosking, J.R.M., Algorithm AS 215: maximum-likelihood estimation of the parameters of the generalized extreme-value distribution, J. R. stat. soc., ser. C: appl. stat., 34, 301-310, (1985)
[5] Hosking, J.R.M., L-moments: analysis and estimation of distributions using linear combinations of order statistics, J. R. stat. soc. ser. B, 52, 105-124, (1990) · Zbl 0703.62018
[6] Hosking, J.R.M., The four-parameter kappa distribution, IBM J. res. dev., 38, 251-258, (1994) · Zbl 0811.60014
[7] Landwehr, J.M.; Matalas, N.C., Quantile estimation with more or less floodlike distributions, Water resour. res., 16, 547-555, (1980)
[8] Martins, E.S.; Stedinger, J.R., Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data, Water resour. res., 36, 737-744, (2000)
[9] Prescott, P.; Walden, A.T., Maximum likelihood estimation of the parameters of the three-parameter generalized extreme-value distribution from censored samples, J. stat. comput. simul., 16, 241-250, (1983) · Zbl 0501.62016
[10] Verhoeven, P.; McAleer, M., Fat tails and asymmetry in financial volatility models, Math. comp. simul., 64, 351-361, (2004) · Zbl 1062.91040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.