Bias and size corrections in extreme value modeling

References

• Baker, D.N., X. Li, A. Pulkkinen, C. M. Ngwira, M. L. Mays, A. B. Galvin, and K. D. C. Simunac. 2013. A major solar eruptive event in July 2012: Defining extreme space weather scenarios. Space Weather 11:585–91.
   Web of Science ®Google Scholar
• Bartlett, M.S. 1937. Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 160:268–82.
   Google Scholar
• Castillo, E., and A. S. Hadi. 1997. Fitting the generalized Pareto distribution to data. Journal of the American Statistical Association 92:1609–20.
   Web of Science ®Google Scholar
• Coles, S. 2001. An introduction to statistical modeling of extreme values. London: Springer Science.
   Google Scholar
• Coles, S.G., and M. J. Dixon. 1999. Likelihood-based inference for extreme value models. Extremes 2:5–23.
   Google Scholar
• Cordeiro, G.M., and S. L. de Paula Ferrari. 1991. A modified score test statistic having chi-squared distribution to order N−1. Biometrika 78:573–82.
   Web of Science ®Google Scholar
• Cordeiro, G.M., and R. Klein. 1994. Bias correction in ARMA models. Statistics & Probability Letters 19:169–76.
   Web of Science ®Google Scholar
• Cox, D.R., and E. J. Snell. 1968. A general definition of residuals. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 30:248–75.
   Web of Science ®Google Scholar
• Efron, B. 1981. Nonparametric standard errors and confidence intervals. Canadian Journal of Statistics 9:139–58.
   Google Scholar
• Efron, B. 1987. Better bootstrap confidence intervals. Journal of the American Statistical Association 82:171–85.
   Web of Science ®Google Scholar
• Giles, D.E., H. Feng, and R. T. Godwin. 2016. Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution. Communications in Statistics – Theory and Methods 45:2465–83.
   Web of Science ®Google Scholar
• Gopalswamy, N. 2006. Coronal mass ejections of solar cycle 23. Journal of Astrophysics and Astronomy 27:243–54.
   Web of Science ®Google Scholar
• Horowitz, J.L. 2001. The bootstrap. Handbook of econometrics 5:3159–228.
   Google Scholar
• Hosking, J.R.M., and J. R. Wallis. 1987. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29:339–49.
   Web of Science ®Google Scholar
• 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 27:251–61.
   Web of Science ®Google Scholar
• Kataoka, R. 2013. Probability of occurrence of extreme magnetic storms. Space Weather 11:214–18.
   Web of Science ®Google Scholar
• Landwehr, J.M., N. C. Matalas, and J. R. Wallis. 1979. Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles. Water Resources Research 15:1055–64.
   Web of Science ®Google Scholar
• Pickands, J. 1975. Statistical inference using extreme order statistics. Annals of Statistics 3:119–31.
   Web of Science ®Google Scholar
• Riley, P. 2012. On the probability of occurrence of extreme space weather events. Space Weather 10:S02012.
   Web of Science ®Google Scholar
• Siscoe, G., N. U. Crooker, and C. R. Clauer. 2006. Dst of the Carrington storm of 1859. Advances in Space Research 38:173–79.
   Web of Science ®Google Scholar
• Thomson, A.W.P., E. B. Dawson, and S. J. Reay. 2011. Quantifying extreme behavior in geomagnetic activity. Space Weather 9:S10001.
   Web of Science ®Google Scholar
• Tsubouchi, K., and Y. Omura. 2007. Long-term occurrence probabilities of intense geomagnetic storm events. Space Weather 5:S12003.
   Web of Science ®Google Scholar
• Weissman, I. 1978. Estimation of parameters and large quantiles based on the K largest observations. Journal of the American Statistical Association 73:812–15.
   Web of Science ®Google Scholar
• Zhang, J. 2007. Likelihood moment estimation for the generalized Pareto distribution. Australian & New Zealand Journal of Statistics 49:69–77.
   Web of Science ®Google Scholar
• Zhang, J., and M. A. Stephens. 2009. A new and efficient estimation method for the generalized Pareto distribution. Technometrics 51:316–25.
   Web of Science ®Google Scholar