Skip to main content
Log in

On testing extreme value conditions

  • Published:
Extremes Aims and scope Submit manuscript

Abstract

Applications of univariate extreme value theory rely on certain as- sumptions. Recently, two methods for testing these extreme value conditions are derived by [Dietrich, D., de Haan, L., Hüsler, J., Extremes 5: 71–85, (2002)] and [Drees, H., de Haan, L., Li, D., J. Stat. Plan. Inference, 136: 3498–3538, (2006)]. In this paper we compare the two tests by simulations and investigate the effect of a possible weight function by choosing a parameter, the test error and the power of each test. The conclusions are useful for extreme value applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • 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)

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jürg Hüsler.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hüsler, J., Li, D. On testing extreme value conditions. Extremes 9, 69–86 (2006). https://doi.org/10.1007/s10687-006-0025-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10687-006-0025-8

Keywords

AMS 2000 Subject Classification

Navigation