A Dependent Lindeberg Central Limit Theorem for Cluster Functionals on Stationary Random Fields

Mathematics

Christophe Chesneau¹  JoséG. Gómez-García¹ 

[1] UNICAEN, CNRS, LMNO, Laboratory of Mathematics Nicolas Oresme, UFR des Sciences, Bld Maréchal Juin, Campus 2, Normandie Université, 14032 Caen, France;

关键词: central limit theorem;    cluster functional;    weak dependence;    Lindeberg method;    extremogram;   

DOI  :  10.3390/math9030212

来源: DOAJ

【 摘 要 】

In this paper, we provide a central limit theorem for the finite-dimensional marginal distributions of empirical processes ${\left(Z_n\left(f\right)\right)}_{f\in \mathcal{F}}$ whose index set $\mathcal{F}$ is a family of cluster functionals valued on blocks of values of a stationary random field. The practicality and applicability of the result depend mainly on the usual Lindeberg condition and on a sequence $T_n$ which summarizes the dependence between the blocks of the random field values. Finally, in application, we use the previous result in order to show the Gaussian asymptotic behavior of the proposed iso-extremogram estimator.

【 授权许可】

Unknown