scholarly journals Asymptotic Properties of Maximum Likelihood Estimates in the Mixed Poisson Model

1984 ◽  
Vol 12 (4) ◽  
pp. 1388-1399 ◽  
Author(s):  
Diane Lambert ◽  
Luke Tierney
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Properties ◽  
Poisson Model ◽  
Maximum Likelihood Estimates

Adaptive control of a production-inventory system

1981 ◽  
Vol 18 (1) ◽  
pp. 204-215 ◽  
Author(s):  
Bharat T. Doshi
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Properties ◽  
Inventory System ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
True Value ◽  
Adaptive Policy ◽  
Production Inventory ◽  
Production Inventory System

We study a production-inventory system in which input is deterministic, and its rate is the controlled parameter. The output is a compound Poisson process with exponential jump-size distribution. The parameters of the output process are unknown. The following adaptive policy is used: At each time t the unknown parameters are estimated by maximum likelihood method and the input rate which would be optimal if these were the true values of the parameter is used. The issues investigated are (1) the convergence of maximum likelihood estimates to the true value, and (2) the asymptotic properties of the cost under the adaptive policy.

Adaptive control of a production-inventory system

1981 ◽  
Vol 18 (01) ◽  
pp. 204-215
Author(s):  
Bharat T. Doshi
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Properties ◽  
Inventory System ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
True Value ◽  
Adaptive Policy ◽  
Production Inventory ◽  
Production Inventory System

We study a production-inventory system in which input is deterministic, and its rate is the controlled parameter. The output is a compound Poisson process with exponential jump-size distribution. The parameters of the output process are unknown. The following adaptive policy is used: At each time t the unknown parameters are estimated by maximum likelihood method and the input rate which would be optimal if these were the true values of the parameter is used. The issues investigated are (1) the convergence of maximum likelihood estimates to the true value, and (2) the asymptotic properties of the cost under the adaptive policy.

scholarly journals Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in GaGLM

2021 ◽  
Author(s):  
Benchao Wang ◽  
Hong Gu ◽  
Pan Qin
Keyword(s):  
Maximum Likelihood ◽  
Gamma Distribution ◽  
Theoretical Foundation ◽  
Asymptotic Properties ◽  
Information Matrix ◽  
Maximum Likelihood Estimates ◽  
Theoretical Research ◽  
Order Moment ◽  
Interval Estimates ◽  
Application Condition

This paper theoretically investigates the asymptotic properties of maximum likelihood estimates of GaGLM, and discusses some properties about Gamma distribution. It can provide theoretical foundation for expanding the application scope of gamma distribution based regression model, and benefit the further interval estimates, hypothesis tests and stochastic control design.The existence of the Gamma function in Gamma distribution makes correlation analysis certain specificity, and few researchers do relevant theoretical research. To complement this part, we established the asymptotic properties and the application condition of maximum likelihood estimates of GaGLM. In addition to this, we also discussed the propertis of the Fisher information matrix ,and n-order moment of Z and log(Z).

scholarly journals Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in GaGLM

2021 ◽  
Author(s):  
Benchao Wang ◽  
Hong Gu ◽  
Pan Qin
Keyword(s):  
Maximum Likelihood ◽  
Gamma Distribution ◽  
Theoretical Foundation ◽  
Asymptotic Properties ◽  
Information Matrix ◽  
Maximum Likelihood Estimates ◽  
Theoretical Research ◽  
Order Moment ◽  
Interval Estimates ◽  
Application Condition

This paper theoretically investigates the asymptotic properties of maximum likelihood estimates of GaGLM, and discusses some properties about Gamma distribution. It can provide theoretical foundation for expanding the application scope of gamma distribution based regression model, and benefit the further interval estimates, hypothesis tests and stochastic control design.The existence of the Gamma function in Gamma distribution makes correlation analysis certain specificity, and few researchers do relevant theoretical research. To complement this part, we established the asymptotic properties and the application condition of maximum likelihood estimates of GaGLM. In addition to this, we also discussed the propertis of the Fisher information matrix ,and n-order moment of Z and log(Z).

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