Extreme Value Theory

Michael Falk (), Jürg Hüsler () and Rolf-Dieter Reiss ()
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Michael Falk: University of Würzburg, Institute of Mathematics
Jürg Hüsler: University of Berne, Department of Mathematical Statistics and Actuarial Science
Rolf-Dieter Reiss: University of Siegen, Department of Mathematics

Chapter Chapter 2 in Laws of Small Numbers: Extremes and Rare Events, 2011, pp 25-101 from Springer

Abstract: 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 δ-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).

Keywords: Generalize Pareto Distribution; Remainder Function; Class Index; Hill Estimator; Left Neighborhood (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0009-9_2

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DOI: 10.1007/978-3-0348-0009-9_2

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