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August 1998 On the distribution of tail array sums for strongly mixing stationary sequences
M. Ross Leadbetter, Holger Rootzén, Laurens de Haan
Ann. Appl. Probab. 8(3): 868-885 (August 1998). DOI: 10.1214/aoap/1028903454


This paper concerns the asymptotic distributions of "tail array" sums of the form $\Sigma \Psi_n (X_i - u_n)$ where ${X_i}$ is a strongly mixing stationary sequence, $\Psi_n$ are real functions which are constant for negative arguments, $\Psi_n (x) = \Psi_n (X_+)$ and ${u_n}$ are levels with $u_n \to \infty$. Compound Poisson limits for rapid convergence of $u_n \to \infty (nP{X_1 > u_n} \to \tau < \infty)$ are considered briefly and a more detailed account given for normal limits applicable to slower rates $(nP(X_1 > u_n) \to \infty)$. The work is motivated by (1) the modeling of "damage" due to very high and moderately high extremes and (2) the provision of probabilistic theory for application to problems of "tail inference" for stationary sequences.


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M. Ross Leadbetter. Holger Rootzén. Laurens de Haan. "On the distribution of tail array sums for strongly mixing stationary sequences." Ann. Appl. Probab. 8 (3) 868 - 885, August 1998.


Published: August 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0939.60007
MathSciNet: MR1627799
Digital Object Identifier: 10.1214/aoap/1028903454

Primary: 60F05
Secondary: 60G10 , 60G70

Keywords: compound Poisson convergence , damage modeling , Extreme values , Mixing central limit theorems , tail inference

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.8 • No. 3 • August 1998
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