Dependent Lindeberg CLT - Finite Dimensional for Empirical Processes of Cluster Functionals
Probability
2015-11-24 v2
Abstract
Drees and Rootz\'en [2010] have proven central limit theorems (CLT) for empirical processes of extreme values cluster functionals built from -mixing processes. The problem with this family of -mixing processes is that it is quite restrictive, as has been shown by Andrews [1984]. We expand this result to a more general dependent processes family, known as weakly dependent processes in the sense of Doukhan and Louhichi [1999], but in finite-dimensional convergence (fidis). We show an example where the application of the CLT-fidis is sufficient in several cases, including a small simulation of the extremogram introduced by Davis and Mikosch [2009] to confirm the efficacy of our result.
Cite
@article{arxiv.1404.4989,
title = {Dependent Lindeberg CLT - Finite Dimensional for Empirical Processes of Cluster Functionals},
author = {José Gregorio Gómez},
journal= {arXiv preprint arXiv:1404.4989},
year = {2015}
}