The Annals of Applied Probability

On the distribution of tail array sums for strongly mixing stationary sequences

M. Ross Leadbetter, Holger Rootzén, and Laurens de Haan

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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.

Article information

Ann. Appl. Probab., Volume 8, Number 3 (1998), 868-885.

First available in Project Euclid: 9 August 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G70: Extreme value theory; extremal processes 60G10: Stationary processes

Mixing central limit theorems compound Poisson convergence damage modeling tail inference extreme values


Rootzén, Holger; Leadbetter, M. Ross; de Haan, Laurens. On the distribution of tail array sums for strongly mixing stationary sequences. Ann. Appl. Probab. 8 (1998), no. 3, 868--885. doi:10.1214/aoap/1028903454.

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