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{1028903454,
author = {Rootz\'en, Holger and Leadbetter, M. Ross and de Haan, Laurens},
title = {On the distribution of tail array sums for strongly mixing
stationary sequences},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 868-885},
language = {en},
url = {http://dml.mathdoc.fr/item/1028903454}
}
Rootzén, Holger; Leadbetter, M. Ross; de Haan, Laurens. On the distribution of tail array sums for strongly mixing
stationary sequences. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 868-885. http://gdmltest.u-ga.fr/item/1028903454/