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A convergence rate in extreme-value theory

Published online by Cambridge University Press:  14 July 2016

A. A. Balkema  and
L. De Haan
A. A. Balkema*
Affiliation:
Universiteit van Amsterdam
L. De Haan*
Affiliation:
Erasmus Universiteit Rotterdam
*
∗Postal address: Mathematisch Institut, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands.
∗∗Postal address: Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000DR Rotterdam, The Netherlands.
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Abstract

A uniform convergence rate is determined for maxima of i.i.d. random variables from a distribution in the domain of attraction of the double-exponential distribution. The result is proved under a second-order condition on the underlying distribution parallelling the one given in Smith (1982) for the domain of attraction of the bounded-below and bounded-above families of limit distributions.

Keywords

SAMPLE EXTREMESDOUBLE-EXPONENTIAL DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 577 - 585
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

De Haan acknowledges partial support from NSF Grant MCS 8202335 and from Colorado State University. Both authors are grateful for the hospitality of CSU, Department of Statistics.

References

Beirlant, J. and Willekens, E. (1990) Rapid variation and rates of convergence. Adv. Appl. Prob. 22(4).CrossRefGoogle Scholar
Cohen, J. P. (1982) Convergence rates for the ultimate and penultimate approximation in extreme-value theory. Adv. Appl. Prob. 14, 833–854.CrossRefGoogle Scholar
Dekkers, A. L. and De Haan, L. (1989) On the estimation of the extreme-value index and large quantile estimation. Ann. Statist. 17, 1795–1832.CrossRefGoogle Scholar
Hall, P. (1979) On the rate of convergence of normal extremes. J. Appl. Prob. 16, 433–439.CrossRefGoogle Scholar
Omey, E. and Willekens, E. (1987) ?-variation with remainder. J. London Math. Soc. 37(2), 105–118.Google Scholar
Resnick, S. I. (1988) Uniform rates of convergence to extreme-value distributions. In Probability in Statistics; Essays in honor of Franklin A. Graybill, ed. Srivastava, J., North-Holland, Amsterdam.Google Scholar
Smith, R. L. (1982) Uniform rates of convergence in extreme-value theory. Adv. Appl. Prob. 14, 600–622.Google Scholar