Tail Empirical Processes Under Mixing Conditions

Holger Drees ()
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Holger Drees: Saarland University, Faculty of Mathematics and Computer Science

A chapter in Empirical Process Techniques for Dependent Data, 2002, pp 325-342 from Springer

Abstract: Abstract Limit theorems for tail processes of absolutely regular time series are surveyed. First we discuss Rootzén’s [29] result on the uniform tail empirical process and generalizations thereof. Then similar results on the uniform tail quantile process are derived. If the observations come from a distribution function that belongs to the domain of attraction of an extreme value distribution, then one can prove weighted approximations of the linearly standardized tail quantile function. Moreover, asymptotic normality can be deduced for many estimators of interest in extreme value statistics. Finally, we apply the limit theorems to particular linear and nonlinear time series models.

Keywords: Limit Theorem; Asymptotic Normality; Empirical Process; Uniform Random Variable; Extreme Observation (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0099-4_12

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DOI: 10.1007/978-1-4612-0099-4_12

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