Abstract
In this chapter we summarize results in extreme value theory, which are primarily based on the condition that the upper tail of the underlying df is in the δ-neighborhood of a generalized Pareto distribution (GPD). This condition, which looks a bit restrictive at first sight (see Section 2.2), is however essentially equivalent to the condition that rates of convergence in extreme value theory are at least of algebraic order (see Theorem 2.2.5). The d-neighborhood is therefore a natural candidate to be considered, if one is interested in reasonable rates of convergence of the functional laws of small numbers in extreme value theory (Theorem 2.3.2) as well as of parameter estimators (Theorems 2.4.4, 2.4.5 and 2.5.4).
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© 2004 Springer Basel AG
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Falk, M., Reiss, RD., Hüsler, J. (2004). Extreme Value Theory. In: Laws of Small Numbers: Extremes and Rare Events. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7791-6_2
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DOI: https://doi.org/10.1007/978-3-0348-7791-6_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2416-2
Online ISBN: 978-3-0348-7791-6
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