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.

scholarly journals A central limit theorem for empirical processes

1982 ◽  
Vol 33 (2) ◽  
pp. 235-248 ◽  
Author(s):  
David Pollard
Keyword(s):  
Stochastic Process ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Empirical Processes ◽  
Empirical Measure ◽  
Integrable Functions ◽  
New Form ◽  
Square Integrable Functions ◽  
Functional Central Limit

AbstractThe empirical measure Pn for independent sampling on a distribution P is formed by placing mass n−1 at each of the first n sample points. In this paper, n½(Pn − P) is regarded as a stochastic process indexed by a family of square integrable functions. A functional central limit theorem is proved for this process. The statement of this theorem involves a new form of combinatorial entropy, definable for classes of square integrable functions.

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