A dependent Lindeberg central limit theorem for cluster functionals on stationary random fields

2020/03/06 by José G. Gómez-García, Gómez-García, José G.
Economics, Econometrics and Finance · Mathematics · #60F05 #60G60 #60G70 #FOS: Mathematics #Financial Risk and Volatility Modeling #Geometry and complex manifolds #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #math.PR #math.ST #msc:60F05 #msc:60G60 #msc:60G70 #stat.TH

paper · pdf · doi:10.48550/arxiv.2003.03280

14 pages

arxiv created 2020/03/06 · openalex publication_date 2020/03/06 · arxiv updated 2020/03/09 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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

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