On testing extreme value conditions

Jürg Hüsler1, Deyuan Li1
1Department of Mathematical Statistics and Actuarial Science, University of Bern, 3012 Bern, Switzerland

Tóm tắt

Từ khóa


Tài liệu tham khảo

Anderson, C.W.: Extreme value theory for a class of discrete distributions with application to some stochastic processes. J. Appl. Probab. 7, 99–113 (1970)

Anderson, C.W., Coles, S., Hüsler, J.: Maxima of Poisson-like variables and related triangular arrays. Ann. Appl. Probab. 7, 953–971 (1997)

Dekkers, A.L.M., de Haan, L., Einmahl, J.H.J.: A moment estimator for the index of an extreme-value distribution. Ann. Stat. 17, 1833–1855 (1989)

Dietrich, D., de Haan, L., Hüsler, J.: Testing extreme value conditions. Extremes 5, 71–85 (2002)

Drees, H., Ferreira, A., de Haan, L.: On the maximum likelihood estimation of the extreme value index. Ann. Appl. Probab. 14, 1179–1201 (2004)

Drees, H., de Haan, L., Li, D.: Approximations to the tail empirical distribution function with application to testing extreme value conditions. J. Stat. Plan. Inference 136, 3498–3538 (2006)

Falk, M., Hüsler, J., Reiss, R.D.: Laws of Small Numbers: Extremes and Rare Events. Birkhäuser, Switzerland (2004)

Geluk, J., de Haan, L.: Regular Variation, Extensions and Tauberian Theorems. CWI Tract 40, Amsterdam (1987)

de Haan, L., Rootzén, H.: On the estimation of high quantiles. J. Stat. Plan. Inference 35, 1–13 (1993)

de Haan, L., Stadtmüller, U.: Generalized regular variation of second order. J. Aust. Math. Soc., Ser. A 61, 381–395 (1996)

Hall, P.: On estimating the endpoint of a distribution. Ann. Stat. 10, 556–568 (1982)

Hill, B.M.: A simple approach to inference about the tail of a distribution. Ann. Stat. 3, 1163–1174 (1975)

Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and Related Properties of Random Sequences and Processes. Springer, Berlin Heidelberg New York (1983)

Nadarajah, S., Mitov, K.: Asymptotics of maxima of discrete random variables. Extremes 5, 287–294 (2003)

Pickands, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119–131 (1975)

Smith, R.L.: Maximum likelihood estimation in a class of nonregular cases. Biometrika 72, 67–90 (1985)