Asymptotic Normality of Hill's Estimator under Weak Dependence

Youcef Berkoun and Karima Boualam

A chapter in Statistical Methodologies from IntechOpen

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.

Keywords: tail index; Hill's estimator; regularly varying function; linear process; weak dependence (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:187638

DOI: 10.5772/intechopen.84555

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