scholarly journals Uniform Asymptotic Normality of the Maximum Likelihood Estimator

1980 ◽  
Vol 8 (6) ◽  
pp. 1375-1381 ◽  
Author(s):  
T. J. Sweeting
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimator

Locally asymptotic normality of Gibbs models on a lattice

1984 ◽  
Vol 16 (03) ◽  
pp. 585-602
Author(s):  
Shigeru Mase
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimator ◽  
Estimation Procedure ◽  
Point Of View ◽  
Normal Families ◽  
Point Pattern ◽  
Likelihood Estimator ◽  
Asymptotic Point ◽  
Statistical Estimation Problem

We consider the statistical estimation problem of potential functions of Gibbs models on the plane lattice. We assume that the area on which a random point pattern is observed is sufficiently large and take an asymptotic point of view. The main result is to show the locally asymptotic normality of the Gibbs model under certain conditions. From this result we can show the optimality of the maximum likelihood estimator employing known results about locally asymptotic normal families, though a practical computation of the maximum likelihood estimator presents difficulties. An estimation procedure based on the method of moments is also proposed.

Locally asymptotic normality of Gibbs models on a lattice

1984 ◽  
Vol 16 (3) ◽  
pp. 585-602 ◽  
Author(s):  
Shigeru Mase
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimator ◽  
Estimation Procedure ◽  
Point Of View ◽  
Normal Families ◽  
Point Pattern ◽  
Likelihood Estimator ◽  
Asymptotic Point ◽  
Statistical Estimation Problem

We consider the statistical estimation problem of potential functions of Gibbs models on the plane lattice. We assume that the area on which a random point pattern is observed is sufficiently large and take an asymptotic point of view. The main result is to show the locally asymptotic normality of the Gibbs model under certain conditions. From this result we can show the optimality of the maximum likelihood estimator employing known results about locally asymptotic normal families, though a practical computation of the maximum likelihood estimator presents difficulties. An estimation procedure based on the method of moments is also proposed.

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