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On large deviation for extremes

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  • Drees, Holger
  • de Haan, Laurens
  • Li, Deyuan

Abstract

Recently, a weighted approximation for the tail empirical distribution function has been developed (Approximations to the tail empirical distribution function with application to testing extreme value conditions. preprint, submitted for publication). We show that the same result can also be used to improve a known uniform approximation of the distribution of the maximum of a random sample. From this a general result about large deviations of this maximum is derived. In addition, the relationship between two second-order conditions used in extreme value theory is clarified.

Suggested Citation

  • Drees, Holger & de Haan, Laurens & Li, Deyuan, 2003. "On large deviation for extremes," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 51-62, August.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:1:p:51-62
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    References listed on IDEAS

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    1. Holger Drees, 1998. "On Smooth Statistical Tail Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 187-210, March.
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    Cited by:

    1. Feng, Bo & Chen, Shouquan, 2015. "On large deviations of extremes under power normalization," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 27-35.
    2. Bücher, Axel & Volgushev, Stanislav & Zou, Nan, 2019. "On second order conditions in the multivariate block maxima and peak over threshold method," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 604-619.

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