Generalized maximum likelihood estimators for the nonstationary generalized extreme value model

Water Resources Research

Volumn 43, Issue 3, 2007, Pages

  El Adlouni, S ^a   Ouarda, T B M J ^a   Zhang, X ^b   Roy, R ^c   Bobee B ^a  

^a CENTRE EAU TERRE ENVIRONNEMENT   (Canada)

^b ENVIRONMENT CANADA   (Canada)

^c OURANOS Consortium on Climate Change ^*  (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD; PARAMETER ESTIMATION;

EXTREME VALUE MODEL; GENERALIZED MAXIMUM LIKELIHOOD ESTIMATION METHOD (GML); SOUTHERN INDEX OSCILLATION;

PRECIPITATION (METEOROLOGY);

COMPUTER SIMULATION; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD; PARAMETER ESTIMATION; PRECIPITATION (METEOROLOGY);

COVARIANCE ANALYSIS; ESTIMATION METHOD; MAXIMUM LIKELIHOOD ANALYSIS; PRECIPITATION ASSESSMENT; SIMULATION; SOUTHERN OSCILLATION;

CALIFORNIA; NORTH AMERICA; UNITED STATES;

EID: 34247577201     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2005WR004545     Document Type: Article

References (37)

1. Aitkin, M., R. J. Boys, and T. J. Chadwick (2005), Bayesian point null hypothesis testing via the posterior likelihood ratio, Stat. Comput., 15, 217-230.
2. Bayarri, M. J., and J. Berger (2000), P-values for composite null models (with discussion), J. Am. Stat. Assoc., 95, 1127-1142.
3. Clarke, R. T. (2002), Estimating trends in data from the Weibull and a generalized extreme value distribution, Water Resour. Res., 38(6), 1089, doi:10.1029/2001WR000575.
4. Coles, G. S. (2001), An Introduction to Statistical Modeling of Extreme Values, 208 pp., Springer, New York.
5. Cunderlik, J. M., and T. B. M. J. Ouarda (2006), Regional flood-duration-frequency modeling in the changing environment, J. Hydrol., 318, 276-291.
6. Dose, V., and A. Menzel (2004), Bayesian analysis of climate change impacts in phenology, Global Change Biol., 10, 259-272, doi:10.111/ j.1529-8817.2003.00731.x.
7. El Adlouni, S., A.-C. Favre, and B. Bobee (2006), Comparison of methodologies to assess the convergence of Markov chain Monte Carlo methods, Comput. Stat. Data Anal., 50(10), 2685-2701.
8. Fisher, R. A., and L. H. C. Tippett (1928), Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proc. Cambridge Philos. Soc., 24, 180-190.
9. Gelman, A., J. Carlin, H. Stern, and D. Rubin (1995), Bayesian Data Analysis, CRC Press, Boca Raton, Fla.
10. Gilks, W., S. Richardson, and D. Spiegelhalter (1996), Markov Chain Monte Carlo Methods in Practice, CRC Press, Boca Raton, Fla.
11. Hamilton, J. (1991), A quasi-Bayesian approach to estimating parameters for mixtures of normal distributions, J. Bus. Econ. Stat., 9, 27-39.
12. Hastings, W. (1970), Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109.
13. Hosking, J. R. M. (1990), L-moments: Analysis and estimation of distributions using linear combinations of order statistics, J. R. Stat. Soc., 52, 105-124.
14. Hosking, J. R. M., J. R. Wallis, and E. F. Wood (1985), Estimation of the generalized extreme-value distribution by the method of probability-weighted moments, Technometrics, 27, 251-261.
15. Intergovernmental Panel on Climate Change (2001), Climate Change 2001: Impacts, Adaptation and Vulnerability, Cambridge Univ. Press, New York.
16. Jain, S., and U. Lall (2001), Floods in a changing climate: Does the past represent the future?, Water Resour. Res., 37, 3193-3205.
17. Jenkinson, A. F. (1955), The frequency distribution of the annual maximum (or minimum) of meteorological elements, Q. J. R. Meteorol. Soc., 81, 158-171.
18. Katz, R. W., M. B. Parlange, and P. Naveau (2002), Statistics of extremes in hydrology, Adv. Water Resour., 25, 1287-1304.
19. Kharin, V. V., and F. W. Zwiers (2005), Estimating extremes in transient climate change simulations, J. Clim., 18, 1156-1173.
20. Leadbetter, M. R., G. Lindgren, and H. Rootzen (1983), Extremes and Related Properties of Random Sequences and Processes, 336 pp., Springer, New York.
21. Madsen, H., P. F. Rasmussen, and D. Rosbjerg (1997), Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events: 1. At-site modeling, Water Resour. Res., 33, 747-758.
22. Martins, E. S., and J. R. Stedinger (2000), Generalized maximum likelihood GEV quantile estimators for hydrologic data, Water Resour. Res., 36, 737-744.
23. Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller (1953), Equations of state calculations by fast computing machines, J. Chem. Phys., 21, 1087-1092.
24. Morrison, J. E., and J. A. Smith (2002), Stochastic modeling of flood peaks using the generalized extreme value (GEV) distribution, Water Resour. Res., 38(12), 1305, doi:10.1029/2001WR000502.
25. Ouarda, T. B. M. J., J. W. Labadie, and D. G. Fontane (1997), Indexed sequential hydrologic modeling for hydropower capacity estimation, J. Am. Water Resour. Assoc., 33, 1337-1349.
26. Ouarda, T. B. M. J., C. Girard, G. Cavadias, and B. Bobee (2001), Regional flood frequency estimation with canonical correlation analysis, J. Hydrol., 254, 157-173.
27. Reis, D. S., and J. R. Stedinger (2005), Bayesian MCMC flood frequency analysis with historical information, J. Hydrol., 313, 97-116.
28. Sankarasubramanian, A., and U. Lall (2003), Flood quantiles in a changing climate: Seasonal forecasts and causal relations, Water Resour. Res., 39(5), 1134, doi:10.1029/2002WR001593.
29. Scarf, P. A. (1992), Estimation for a four parameter generalized extreme value distribution, Commun. Stat. Theory Methods., 21, 2185-2201.
30. Smith, R. L. (1985), Maximum likelihood estimation in a class of non-regular cases, Biometrika, 72, 67-92.
31. Smith, R. L. (1989), Extreme value analysis of environmental time series: An application to trend detection in ground-level ozone (with discussion), Stat. Sci., 4, 367-393.
32. Stedinger, J. R., R. M. Vogel, and E. Foufoula-Georgiou (1993), Frequency analysis of extreme events, in Handbook of Hydrology, edited by D. R. Maidment, pp. 1-66, McGraw-Hill, New York.
33. Venkataraman, S. (1997), Value at risk for a mixture of normal distributions: The use of quasi-Bayesian estimation technique, in Economic Perspectives, pp. 2-13, Fed. Reserve Bank of Chicago, Chicago, Ill.
34. Wang, X. L. and V. Swail (2004), Climate change signal and uncertainty in projections of ocean wave heights, paper presented at 8th International Workshop on Wave Forecast and Hindcast, Environ. Can., Oahu, Hawaii, 14-19 Nov.
35. Wang, X. L., F. W. Zwiers, and V. Swail (2004), North Atlantic Ocean wave climate scenarios for the 21st century, J. Clim., 17, 2368-2383.
36. Zhang, X., K. D. Harvey, W. D. Hogg, and T. R. Yuzyk (2001), Trends in Canadian streamflow, Water Resour. Res., 37, 987-999.
37. Zhang, X., F. W. Zweirs, and G. Li (2004), Monte Carlo experiments on the detection of trends in extreme values, J. Clim., 17, 1945-1952.