scholarly journals Central limit theorems for smoothed extreme value estimates of Poisson point processes boundaries

2005 ◽  
Vol 135 (2) ◽  
pp. 433-460 ◽  
Author(s):  
Stéphane Girard ◽  
Ludovic Menneteau
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Point Processes ◽  
Extreme Value ◽  
Central Limit Theorems ◽  
Poisson Point Processes

scholarly journals Central limit theorems for $U$-statistics of Poisson point processes

2013 ◽  
Vol 41 (6) ◽  
pp. 3879-3909 ◽  
Author(s):  
Matthias Reitzner ◽  
Matthias Schulte
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Point Processes ◽  
Central Limit Theorems ◽  
Poisson Point Processes ◽  
U Statistics

Statistics of the Boolean model: from the estimation of means to the estimation of distributions

1995 ◽  
Vol 27 (01) ◽  
pp. 63-86 ◽  
Author(s):  
Ilya S. Molchanov
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Point Processes ◽  
Boolean Model ◽  
Higher Order ◽  
Central Limit Theorems ◽  
The Mean ◽  
Estimation Of Distributions ◽  
Non Parametric

Non-parametric estimators of the distribution of the grain of the Boolean model are considered. The technique is based on the study of point processes of tangent points in different directions related to the Boolean model. Their second- and higher-order characteristics are used to estimate the mean body and the distribution of the typical grain. Central limit theorems for the improved estimator of the intensity and surface measures of the Boolean model are also proved.

Statistics of the Boolean model: from the estimation of means to the estimation of distributions

1995 ◽  
Vol 27 (1) ◽  
pp. 63-86 ◽  
Author(s):  
Ilya S. Molchanov
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Point Processes ◽  
Boolean Model ◽  
Higher Order ◽  
Central Limit Theorems ◽  
The Mean ◽  
Estimation Of Distributions ◽  
Non Parametric

Non-parametric estimators of the distribution of the grain of the Boolean model are considered. The technique is based on the study of point processes of tangent points in different directions related to the Boolean model. Their second- and higher-order characteristics are used to estimate the mean body and the distribution of the typical grain. Central limit theorems for the improved estimator of the intensity and surface measures of the Boolean model are also proved.

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