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).

scholarly journals The Exponentiated Lindley Geometric Distribution with Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 510
Author(s):  
Bo Peng ◽  
Zhengqiu Xu ◽  
Min Wang
Keyword(s):  
Maximum Likelihood ◽  
Geometric Distribution ◽  
Residual Life ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters

We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.

Large-Sample Inference of EM Based on Maximum Likelihood Estimates

2014 ◽  
Vol 1049-1050 ◽  
pp. 1343-1346
Author(s):  
Yong Li
Keyword(s):  
Data Analysis ◽  
Missing Data ◽  
Maximum Likelihood ◽  
Em Algorithm ◽  
Information Matrix ◽  
Maximum Likelihood Estimates ◽  
Large Sample ◽  
Missing Data Analysis ◽  
And Inversion

EM algorithm is a very popular algorithm in missing data analysis. However,The variance of the estimator from EM is intractable. In this paper, we propose the supplemented EM algorithm for computing the variance that do not require computation and inversion of the information matrix.

Minimum variance and the estimation of several parameters

1947 ◽  
Vol 43 (2) ◽  
pp. 280-283 ◽  
Author(s):  
C. Radhakrishna Rao
Keyword(s):  
Maximum Likelihood ◽  
Information Matrix ◽  
Minimum Variance ◽  
Maximum Likelihood Estimates ◽  
Dispersion Matrix ◽  
Minimal Set ◽  
Sufficient Statistics ◽  
Large Samples ◽  
Method Of Maximum Likelihood ◽  
Unbiased Estimates

With the help of certain inequalities concerning the elements of the dispersion matrix of a set of statistics, and of the information matrix, the following results have been proved. Some of these inequalities are extensions of results given by Fisher (1) in the case of a single parameter.(i) Efficient statistics are explicit functions of the minimal set of sufficient statistics.(ii) Functions of the minimal set of sufficient statistics, satisfying the property of uniqueness defined in the text, are best unbiased estimates. Under certain conditions estimates possessing exactly the minimum possible variance can be obtained by the method of maximum likelihood.(iii) In large samples maximum likelihood estimates supply efficient statistics in the case of several parameters.(iv) The importance of replacing the sample by an exhaustive set of sufficient statistics (referred to in this paper as the minimal set) as a first step in any methodological problem has been stressed by R. A. Fisher in various articles and lectures. The above discussion supplies a formal demonstration of this view so far as the problem of estimation is concerned.

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