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Uniform rates of convergence in extreme-value theory

Published online by Cambridge University Press:  01 July 2016

Richard L. Smith
Richard L. Smith*
Affiliation:
Imperial College, London
*
∗Postal address: Department of Mathematics, Imperial College of Science and Technology, Huxley Building, Queen's Gate, London SW7 2BZ, U.K.
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Abstract

Rates of convergence are derived for the convergence in distribution of renormalised sample maxima to the appropriate extreme-value distribution. Related questions which are discussed include the estimation of the principal error term and the optimality of the renormalising constants. Throughout the paper a close parallel is drawn with the theory of slow variation with remainder. This theory is used in proving most of the results. Some applications are discussed, including some models of importance in reliability.

Keywords

EXTREME-VALUE THEORYRATES OF CONVERGENCESLOW VARIATION WITH REMAINDER
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 3 , September 1982 , pp. 600 - 622
Copyright
Copyright © Applied Probability Trust 1982 

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