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Asymptotic Normality of Hill's Estimator under Weak Dependence

In: Statistical Methodologies

Author

Listed:
  • Youcef Berkoun
  • Karima Boualam

Abstract

This note is devoted to the asymptotic normality of Hill's estimator when data are weakly dependent in the sense of Doukhan. The primary results on this setting rely on the observations being strong mixing. This assumption is often the key tool for establishing the asymptotic behavior of this estimator. A number of attempts have been made to relax the assumption of stationarity and mixing. Relaxing this condition, and assuming the weak dependence, we extend the results obtained by Rootzen and Starica. This approach requires less restrictive conditions than the previous results.

Suggested Citation

  • Youcef Berkoun & Karima Boualam, 2020. "Asymptotic Normality of Hill's Estimator under Weak Dependence," Chapters, in: Jan Peter Hessling (ed.), Statistical Methodologies, IntechOpen.
    • Handle: RePEc:ito:pchaps:187638
    DOI: 10.5772/intechopen.84555
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    More about this item

    Keywords

    tail index; Hill's estimator; regularly varying function; linear process; weak dependence;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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