Dependent Lindeberg central limit theorem for the fidis of empirical processes of cluster functionals

Statistics ◽  
2018 ◽  
Vol 52 (5) ◽  
pp. 955-979 ◽  
Author(s):  
José G. Gómez
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Empirical Processes

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

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 212
Author(s):  
José G. Gómez-García ◽  
Christophe Chesneau
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Field ◽  
Central Limit ◽  
Random Fields ◽  
Empirical Processes ◽  
Index Set ◽  
Finite Dimensional ◽  
Lindeberg Condition ◽  
Stationary Random Field

In this paper, we provide a central limit theorem for the finite-dimensional marginal distributions of empirical processes (Zn(f))f∈F 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 depend mainly on the usual Lindeberg condition and on a sequence Tn 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.

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