Balan, Raluca Louhichi, Sana

In this article, we consider a sequence (N n ) n≥1 of point processes, whose points lie in a subset E of R\{0} and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient conditions for the convergence in the distribution of (N_n) n≥1 to an infinitely divisible point process N. As applications, we discuss t...

Bertail, Patrice Clémençon, Stéphan Tressou, Jessica
Published in
Extremes

This paper is devoted to the study of specific statistical methods for extremal events in the markovian setup, based on the regenerative method and the Nummelin technique. Exploiting ideas developed in Rootzén (Adv Appl Probab 20:371–390, 1988), the principle underlying our methodology consists of first generating a random number l of approximate p...

Bertail, Patrice Clemencon, Stephan Tressou-Cosmao, Jessica

This paper is devoted to show how the regenerative block-bootstrap methodology (RBB), proved asymptotically valid in the case of sample means and U-statistics based on data drawn from a regenerative arkov chain X = {Xn}n in Bertail and Clemencon (2005, 2006b), may be successfully extended for onstructing confidence intervals for the extremal index ...

Bertail, Patrice Clémençon, Stéphan Tressou, Jessica

This paper is devoted to show how the regenerative block-bootstrap methodology (RBB), proved asymptotically valid in the case of sample means and U-statistics based on data drawn from a regenerative arkov chain X = {Xn}n in Bertail and Clemencon (2005, 2006b), may be successfully extended for onstructing confidence intervals for the extremal index ...

Bertail, Patrice Clémençon, Stéphan Tressou, Jessica

This paper is devoted to the study of specific statistical methods for extremal events in the markovian setup, based on the regenerative method and the Nummelin technique. Exploiting ideas developed in [53], the principle underlying our methodology consists in generating first (a random number l of) approximate pseudo-renewal times 1, 2, . . . , l ...

Hall, A. Scotto, M. G. Ferreira, H.
Published in
Extremes

Let {Xk} be a stationary moving average sequence of the form Xk = Σj = −∞∞βj*Zk − j where {Zk} is an iid sequence of random variables with regularly varying tails, and the operator * denotes multiplication if Zk is continuous and binomial thinning if Zk is a non-negative integer-valued. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepac...

Laurini, Fabrizio Tawn, Jonathan A.
Published in
Extremes

New methods for identifying clusters of extreme values are proposed that exploit additional knowledge of the trajectory of the process around extreme events. These methods lead directly to new estimators of cluster characteristics, such as the extremal index, which are shown to have both substantially reduced bias and greater insensitivity to clust...

Hall, Andreia
Published in
Extremes

In this paper we study the limiting distribution of the maximum term of non-negative integer-valued moving average sequences of the form Xn = ∑i = −∞∞ βi ○ Zn − i where { Zn} is an iid sequence of non-negative integer-valued random variables with regularly varying tails, βi○Zn−i denotes binomial thinning. Several models are considered allowing diff...

Ancona-Navarrete, Miguel A. Tawn, Jonathan A.
Published in
Extremes

The extremal index, θ (0≤θ≤1), is the key parameter when extending discussions of the limiting behavior of the extreme values from independent and identically distributed sequences to stationary sequences. As θ measures the limiting dependence of exceedances over a threshold u, as u tends to the upper endpoint of the distribution, it may not always...

Hu¨sler, Ju¨rg
Published in
Extremes

Consider a triangular array of standard Gaussian random variables {ζn,i, i ≥ 0, n≥ 1} such that {ζn,i, i ≥ 0} is a stationary normal sequence for each n ≥ 1. Let ρn,k = corr(ζn,i,ζn,i+k). If (1-ρn,k)log n → δk ∈ (0,∞) as n → ∞ for some k, then the locations where the extreme values occur cluster and the limiting distribution of the maxima is still ...