Parameter Estimation for the Tail Distribution of a Random Sequence

References

• Beirlant , J. , Goegebeur , Y. , Segers , J. and Teufel , J. 2004 . Statistics of Extremes—Theory and Applications (Wiley Series in Probability and Statistics) , Chichester : Wiley .
   Google Scholar
• Busing , F. M. T. , Meijer , E. and van der Leeden , R. 1999 . Delete-m jackknife for unequal m . Statistics and Computation , 9 : 3 – 8 .
   Web of Science ®Google Scholar
• Ceppi , P. , Della-Marta , P. M. and Appenzeller , C. 2008 . Extreme Value Analysis of Wind Speed Observations over Switzerland , Arbeitsbericht MeteoSchweiz Nr. 219 Zurich : Bundesamt für Meteorologie und Klimatologie, MeteoSchweiz .
   Google Scholar
• Coles , S. 2001 . An Introduction to Statistical Modelling of Extreme Values , Springer Series in Statistics London : Springer .
   Google Scholar
• de Haan , L. and Ferreira , A. 2006 . Extreme Value Theory—An Introduction , New York : Springer .
   Google Scholar
• Deheuvels , P. 1983 . Point process and multivariate extreme value . Journal of Multivariate Analysis , 13 : 257 – 272 .
   Web of Science ®Google Scholar
• Dekkers , A. L. M. , Einmahl , J. H. J. and de Haan , L. 1989 . A moment estimator for the index of an extreme-value distribution . The Annals of Statistics , 17 : 1833 – 1855 .
   Web of Science ®Google Scholar
• Efron , B. 1979 . Bootstrap methods: Another look at the jackknife . The Annals of Statistics , 7 : 1 – 26 .
   Web of Science ®Google Scholar
• Hosking , J. R. M. , Wallis , J. R. and Wood , E. F. 1985 . Estimation of the generalized extreme value distribution by the method of probability-weighted moments . Technometrics , 27 : 251 – 261 .
   Web of Science ®Google Scholar
• Hüsler , J. , Li , D. and Raschke , M. 2011 . Estimation for the generalized Pareto distribution using maximum likelihood and goodness of fit . Communications in Statistics—Theory and Methods , 40 : 2500 – 2510 .
   Web of Science ®Google Scholar
• Joe , H. 1997 . Multivariate Models and Dependence Concepts , London, New York : Chapman and Hall .
   Google Scholar
• Leadbetter , M. R. , Lindgren , G. and Rootzén , H. 1983 . Extremes and Related Properties of Random Sequences and Processes. Springer-Series in Statistics , New York, Heidelberg, Berlin : Springer .
   Google Scholar
• Leadbetter , M. R. , Weissman , I. , de Haan , L. and Rootzén , H. 1989 . “ On clustering of high values in statistically stationary series ” . In Proceedings of the 4th International Meeting on Statistical Climatology , Edited by: Sanson , J. 217 – 222 . Wellington : New Zealand Meteorological Service .
   Google Scholar
• Mari , D. D. and Kotz , S. 2001 . Correlation and Dependence , London : Imperial College Press .
   Google Scholar
• Miller , R. G. 1974 . The jackknife—A review . Biometrika , 61 : 1 – 15 .
   Web of Science ®Google Scholar
• Pickands , J. 1975 . Statistical inference using extreme order statistics . The Annals of Statistics , 3 : 119 – 131 .
   Web of Science ®Google Scholar
• Quenouille , M. H. 1949 . Approximate tests of correlation in time-series . Journal of the Royal Statistical Society: Series B , 11 : 68 – 84 .
   Google Scholar
• Quenouille , M. H. 1956 . Notes on bias in estimation . Biometrika , 43 : 353 – 360 .
   Web of Science ®Google Scholar
• Raschke , M. 2012 . Inference for the truncated exponential distribution . Stochastic Environmental Research and Risk Assessment , 26 : 127 – 138 .
   Web of Science ®Google Scholar
• Shao , J. and Tu , D. 1995 . The Jackknife and Bootstrap , Springer Series in Statistics New York : Springer .
   Google Scholar
• Smith , R. J. 1985 . Maximum likelihood estimation in a class of nonregular cases . Biometrika , 72 : 67 – 90 .
   Web of Science ®Google Scholar
• Smith , R. L. 1984 . “ Threshold methods for sample extremes ” . In Statistical Extremes and Applications , Edited by: Oliveira , Tiago de . 621 – 638 . Dordrecht : J. D. Reidel .
   Google Scholar
• Tukey , J. W. 1958 . Bias and confidence in not-quite large samples (Abstract) . The Annals of Mathematical Statistics , 29 : 614
   Google Scholar
• Wolter , K. M. 1985 . Introduction to Variance Estimation , New York : Springer .
   Google Scholar