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Central limit theorems for sums of extreme values

Published online by Cambridge University Press:  24 October 2008

Sándor Csörgoő  and
David M. Mason
Sándor Csörgoő
Affiliation:
Szeged University, Szeged, Hungary
David M. Mason
Affiliation:
University of Delaware, Newark, Delaware, U.S.A.
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Abstract

Given a sequence of non-negative independent and identically distributed random variables, we determine conditions on the common distribution such that the sum of appropriately normalized and centred upper kn extreme values based on the first n random variables converges in distribution to a normal random variable, where kn → ∞ and kn/ n → 0 as n → ∞. The probabilistic problem is motivated by recent statistical work on the estimation of the exponent of a regularly varying distribution function. Our main tool is a new Brownian bridge approximation to the uniform empirical and quantile processes in weighted supremum norms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 3 , November 1985 , pp. 547 - 558
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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