scholarly journals Functional central limit theorem for the volume of excursion sets generated by associated random fields

2011 ◽  
Vol 81 (6) ◽  
pp. 642-646 ◽  
Author(s):  
D. Meschenmoser ◽  
A. Shashkin
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Functional Central Limit Theorem ◽  
Excursion Sets ◽  
Functional Central Limit

scholarly journals A Functional Central Limit Theorem for Kernel Type Density Estimators

2016 ◽  
Vol 35 (4) ◽  
Author(s):  
István Fazekas ◽  
Peter Filzmoser
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Functional Central Limit Theorem ◽  
Integrable Functions ◽  
Square Integrable Functions ◽  
Functional Central Limit ◽  
Kernel Type ◽  
Density Estimators

Kernel type density estimators are studied for random fields. A functional central limit theorem in the space of square integrable functions is proved if the locations of observations become more and more dense in an increasing sequence of domains.

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