scholarly journals Asymptotic normality of the maximum likelihood estimator for cooperative sequential adsorption

2011 ◽  
Vol 43 (3) ◽  
pp. 636-648 ◽  
Author(s):  
Mathew D. Penrose ◽  
Vadim Shcherbakov
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimator ◽  
Time Series Data ◽  
Series Data ◽  
Adsorption Model ◽  
Likelihood Estimator ◽  
Large Samples ◽  
Sequential Adsorption

We consider statistical inference for a parametric cooperative sequential adsorption model for spatial time series data, based on maximum likelihood. We establish asymptotic normality of the maximum likelihood estimator in the thermodynamic limit. We also perform and discuss some numerical simulations of the model, which illustrate the procedure for creating confidence intervals for large samples.

scholarly journals Asymptotic normality of the maximum likelihood estimator for cooperative sequential adsorption

2011 ◽  
Vol 43 (03) ◽  
pp. 636-648
Author(s):  
Mathew D. Penrose ◽  
Vadim Shcherbakov
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimator ◽  
Time Series Data ◽  
Series Data ◽  
Adsorption Model ◽  
Likelihood Estimator ◽  
Large Samples ◽  
Sequential Adsorption

We consider statistical inference for a parametric cooperative sequential adsorption model for spatial time series data, based on maximum likelihood. We establish asymptotic normality of the maximum likelihood estimator in the thermodynamic limit. We also perform and discuss some numerical simulations of the model, which illustrate the procedure for creating confidence intervals for large samples.

scholarly journals Maximum likelihood estimation for cooperative sequential adsorption

2009 ◽  
Vol 41 (04) ◽  
pp. 978-1001 ◽  
Author(s):  
Mathew D. Penrose ◽  
Vadim Shcherbakov
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Thermodynamic Limit ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Current Configuration ◽  
Sequential Adsorption ◽  
Spatial Locations

We consider a model for a time series of spatial locations, in which points are placed sequentially at random into an initially empty region of ℝ d , and given the current configuration of points, the likelihood at location x for the next particle is proportional to a specified function β k of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters β k (assumed to be zero for k exceeding some fixed threshold) is consistent in the thermodynamic limit where the number of points grows in proportion to the size of the region.

scholarly journals Maximum likelihood estimation for cooperative sequential adsorption

2009 ◽  
Vol 41 (4) ◽  
pp. 978-1001 ◽  
Author(s):  
Mathew D. Penrose ◽  
Vadim Shcherbakov
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Thermodynamic Limit ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Current Configuration ◽  
Sequential Adsorption ◽  
Spatial Locations

We consider a model for a time series of spatial locations, in which points are placed sequentially at random into an initially empty region of ℝd, and given the current configuration of points, the likelihood at location x for the next particle is proportional to a specified function βk of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters βk (assumed to be zero for k exceeding some fixed threshold) is consistent in the thermodynamic limit where the number of points grows in proportion to the size of the region.

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