scholarly journals Central limit theorems for empirical product densities of stationary point processes

2014 ◽  
Vol 17 (2) ◽  
pp. 121-138 ◽  
Author(s):  
Lothar Heinrich ◽  
Stella Klein
Keyword(s):  
Central Limit ◽  
Stationary Point ◽  
Limit Theorems ◽  
Point Processes ◽  
Central Limit Theorems ◽  
Product Densities ◽  
Stationary Point Processes

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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