Uniform central limit theorems for kernel density estimators

2007 ◽  
Vol 141 (3-4) ◽  
pp. 333-387 ◽  
Author(s):  
Evarist Giné ◽  
Richard Nickl
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Kernel Density ◽  
Central Limit Theorems ◽  
Kernel Density Estimators ◽  
Density Estimators

scholarly journals Nonparametric density estimators based on nonstationary absolutely regular random sequences

1996 ◽  
Vol 9 (3) ◽  
pp. 233-254 ◽  
Author(s):  
Michel Harel ◽  
Madan L. Puri
Keyword(s):  
Central Limit ◽  
Markov Processes ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Density Estimator ◽  
Random Sequences ◽  
Arma Processes ◽  
Density Estimators

In this paper, the central limit theorems for the density estimator and for the integrated square error are proved for the case when the underlying sequence of random variables is nonstationary. Applications to Markov processes and ARMA processes are provided.

scholarly journals Pressure Function and Limit Theorems for Almost Anosov Flows

2021 ◽  
Vol 382 (1) ◽  
pp. 1-47
Author(s):  
Henk Bruin ◽  
Dalia Terhesiu ◽  
Mike Todd
Keyword(s):  
Thermodynamic Properties ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Stable Laws ◽  
Analytic Framework ◽  
Pressure Function ◽  
Hyperbolic Flows ◽  
Anosov Flows ◽  
Almost Anosov

AbstractWe obtain limit theorems (Stable Laws and Central Limit Theorems, both standard and non-standard) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function and limit theorems is studied in an abstract functional analytic framework, which may be applicable to other classes of non-uniformly hyperbolic flows.

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