Vector generalized linear and additive extreme value models

Extremes

Volumn 10, Issue 1-2, 2007, Pages 1-19

  Yee, Thomas W ^a   Stephenson, Alec G ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Extreme value modelling; Fisher scoring; Iteratively reweighted least squares; Maximum likelihood estimation; Penalized likelihood; Smoothing; Vector splines

Indexed keywords

EID: 34547887938     PISSN: 13861999     EISSN: 1572915X     Source Type: Journal    
DOI: 10.1007/s10687-007-0032-4     Document Type: Article

References (42)

1. Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J.: Statistics of Extremes. Wiley, Chichester, England (2004)
2. Broyden, C.G.: The convergence of a class of double-rank minimization algorithms. J. Inst. Math. Appl. 6, 76-90 (1970)
3. Buja, A., Hastie, T., Tibshirani, R.: Linear smoothers and additive models (with discussion). Ann. Stat. 17, 453-510 (1989)
4. Chambers, J.M.: Programming with Data: A Guide to the S Language. Springer, New York (1998)
5. Chambers, J.M., Hastie, T.J. (eds.) Statistical Models in S. Chapman & Hall, New York (1993)
6. Chavez-Demoulin, V., Davison, A.C.: Generalized additive modelling of sample extremes. Appl. Stat. 54, 207-222 (2005)
7. Coles, S.: An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London (2001)
8. de Boor, C.: A Practical Guide to Splines. Springer, Berlin (1978)
9. Efron, B., Hinkley, D.V.: Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information. Biometrika 65, 457-481 (1978)
10. Ferro, C.A.T., Segers, J.: Inference for clusters of extreme values. J. R. Stat. Soc., B 65, 545-556 (2003)
11. Fessler, J.A.: Nonparametric fixed-interval smoothing with vector splines. IEEE Trans. Acoust. Speech Signal Process. 39, 852-859 (1991)
12. Green, P.J., Silverman, B.W.: Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Chapman & Hall, London (1994)
13. Hastie, T., Tibshirani, R.: Generalized additive models: some applications. J. Am. Stat. Assoc. 82, 371-386 (1987)
14. Hastie, T.J., Tibshirani, R.J.: Generalized Additive Models. Chapman & Hall, London (1990)
15. Hosking, J.R.M., Wallis, J.R.: Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29, 339-349 (1987)
16. Hosking, J.R.M., Wallis, J.R.: Regional Frequency Analysis. Cambridge University Press, Cambridge, UK (1997)
17. Hosking, J.R.M., Wallis, J.R., Wood, E.F.: Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics 27, 251-261 (1985)
18. Ihaka, R., Gentleman, R.: R: A language for data analysis and graphics. J. Comput. Graph. Stat. 5, 299-314 (1996)
19. Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and Related Properties of Random Sequences and Series. Springer-Verlag, New York (1983)
20. Ledford, A.W., Tawn, J.A.: Statistics for near independence in multivariate extreme values. Biometrika 83, 169-187 (1996)
21. Nelder, J.A., Wedderburn, R.W.M.: Generalized linear models. J. R. Stat. Soc., A, 135, 370-384 (1972)
22. Oakes, D., Manatunga, A.K.: Fisher information for a bivariate extreme value distribution. Biometrika 79, 827-832 (1992)
23. Pauli, F., Coles, S.: Penalized likelihood inference in extreme value analyses. J. Appl. Stat. 28, 547-560 (2001)
24. Pickands, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119-131 (1975)
25. Prescott, P., Walden, A.T.: Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Biometrika 67, 723-724 (1980)
26. Reinsch, C.: Smoothing by spline functions. Numer. Math. 10, 177-183 (1967)
27. Rose, C., Smith, M.D.: Mathematical Statistics with Mathematica. Springer, New York (2002)
28. Rosen, O., Cohen, A.: Extreme percentile regression. In: Härdle, W., Schimek, M.G. (eds.) Statistical Theory and Computational Aspects of Smoothing: Proceedings of the COMPSTAT '94 Satellite Meeting held in Semmering, Austria, August 1994, pp. 27-28. Physica-Verlag, Heidelberg (1996)
29. Schimek, M.G. (ed.): Smoothing and Regression: Approaches, Computation, and Application. Wiley, New York (2000)
30. Shi, D.: Fisher information for a multivariate extreme value distribution. Biometrika 82, 644-649 (1995)
31. Smith, E.L., Walshaw, D.: Modelling bivariate extremes in a region. In: Bernardo, J.M., Bayarri, M.J., Berger, J.O., Dawid, A.P., Heckerman, D., Smith, A.F.M., West, M. (eds.) Bayesian Statistics 7. Oxford University Press, Oxford, UK (2003)
32. Smith, R.L.: Maximum likelihood estimation in a class of nonregular cases. Biometrika 72, 67-90 (1985)
33. Smith, R.L.: Extreme value theory based on the r largest annual events. J. Hydrol. 86, 27-43 (1986)
34. Stephenson, A.G.: evd: Extreme value distributions. R News 2(2), 31-32 (2002)
35. Stephenson, A.G., Gilleland, E.: Software for the analysis of extreme events: the current state and future directions. Extremes 8, 87-109 (2006)
36. Tawn, J.A.: Bivariate extreme value theory: models and estimation. Biometrika 75, 397-415 (1988)
37. Weissman, I.: Estimation of parameters and large quantiles based on the k largest observations. J. Am. Stat. Assoc. 73, 812-815 (1978)
38. Yee, T.W.: The Analysis of Binary Data in Quantitative Plant Ecology. Ph.D. thesis, University of Auckland, Department of Mathematics & Statistics, University of Auckland, New Zealand (1993)
39. Yee, T.W.: Vector splines and other vector smoothers. In: Bethlehem, J.G., van der Heijden, P.G.M. (eds.) Proceedings in Computational Statistics COMPSTAT 2000. Physica-Verlag, Heidelberg (2000)
40. Yee, T.W.: A User's Guide to the vgam Package, http://www.stat.auckland. ac.nz/~yee/VGAM (2007)
41. Yee, T.W., Hastie, T.J.: Reduced-rank vector generalized linear models. Stat. Modelling 3, 15-41 (2003)
42. Yee, T.W., Wild, C.J.: Vector generalized additive models. J. R. Stat. Soc., B 58, 481-493 (1996)