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On the asymptotic normality of Hill's estimator

Published online by Cambridge University Press:  24 October 2008

Sándor Csörgő  and
László Viharos
Sándor Csörgő
Affiliation:
Department of Statistics, University of Michigan, Ann Arbor, MI 48109-1027, U.S.A.
László Viharos
Affiliation:
Bolyai Institute, University of Szeged, 6720 Szeged, Hungary
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Extract

Let X, X1, X2, …, be independent random variables with a common distribution function F(x) = P {X ≤ x}, x∈ℝ, and for each n∈ℕ, let X1, n ≤ … ≤ Xn, n denote the order statistics pertaining to the sample X1, …, Xn. We assume that 1–F(x) = x−1/cl(x), 0 < x < ∞, where l is some function slowly varying at infinity and c > 0 is any fixed number. The class of all such distribution functions will be denoted by .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 2 , September 1995 , pp. 375 - 382
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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