On the maximum likelihood estimator for a discrete multivariate crash frequencies model

2020 ◽  
Vol 15 (2) ◽  
pp. 2335-2348
Author(s):  
Issa Cherif Geraldo
Keyword(s):  
Statistical Analysis ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Road Safety ◽  
Strong Consistency ◽  
Delta Method ◽  
Closed Form Expression ◽  
Parameter Vector ◽  
Form Expression ◽  
Likelihood Estimator

In this paper, we study the maximum likelihood estimator (MLE) of the parameter vector of a discrete multivariate crash frequencies model used in the statistical analysis of the effectiveness of a road safety measure. We derive the closed-form expression of the MLE afterwards we prove its strong consistency and we obtain the exact variance of the components of the MLE except one component whose variance is approximated via the delta method.

Strong Consistency of Maximum Likelihood Estimators n Exponential Sequential Model

2014 ◽  
Vol 519-520 ◽  
pp. 878-882
Author(s):  
Chang Ming Yin ◽  
Bo Hong Chen ◽  
Shuang Hua Liu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Strong Consistency ◽  
Maximum Likelihood Estimators ◽  
Regression Parameter ◽  
Parameter Vector ◽  
Likelihood Estimator ◽  
Sequential Model ◽  
Mild Conditions ◽  
Strongly Consistent

For the exponential sequential model, we show that maximum likelihood estimator of regression parameter vector is asymptotically existence and strongly consistent under mild conditions

scholarly journals Quasi-maximum likelihood estimator of Laplace (1, 1) for GARCH models

2017 ◽  
Vol 15 (1) ◽  
pp. 1539-1548
Author(s):  
Haiyan Xuan ◽  
Lixin Song ◽  
Muhammad Amin ◽  
Yongxia Shi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Strong Consistency ◽  
Garch Model ◽  
Garch Models ◽  
Parameter Vector ◽  
Likelihood Estimator ◽  
Comparison Results ◽  
Quasi Maximum Likelihood ◽  
The Garch Model

Abstract This paper studies the quasi-maximum likelihood estimator (QMLE) for the generalized autoregressive conditional heteroscedastic (GARCH) model based on the Laplace (1,1) residuals. The QMLE is proposed to the parameter vector of the GARCH model with the Laplace (1,1) firstly. Under some certain conditions, the strong consistency and asymptotic normality of QMLE are then established. In what follows, a real example with Laplace and normal distribution is analyzed to evaluate the performance of the QMLE and some comparison results on the performance are given. In the end the proofs of some theorem are presented.

scholarly journals Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies

1993 ◽  
Vol 12 (2) ◽  
pp. 215-231 ◽  
Author(s):  
J. Llacer ◽  
E. Veklerov ◽  
K.J. Coakley ◽  
E.J. Hoffman ◽  
J. Nunez
Keyword(s):  
Statistical Analysis ◽  
Maximum Likelihood ◽  
Human Brain ◽  
Maximum Likelihood Estimator ◽  
Fdg Pet ◽  
Likelihood Estimator

Asymptotic Effect of Misspecification in the Random Part of the Multilevel Model

2004 ◽  
Vol 29 (2) ◽  
pp. 201-218 ◽  
Author(s):  
Johannes Berkhof ◽  
Jarl Kennard Kampen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Variance Components ◽  
Fixed Effects ◽  
Multilevel Model ◽  
Closed Form Expression ◽  
Model Parameters ◽  
Likelihood Estimator ◽  
The Moment ◽  
Random Part

The authors examine the asymptotic effect of omitting a random coefficient in the multilevel model and derive expressions for the change in (a) the variance components estimator and (b) the estimated variance of the fixed effects estimator. They apply the method of moments, which yields a closed form expression for the omission effect. In practice, the model parameters are estimated by maximum likelihood; however, since the moment estimator and the maximum likelihood estimator are both consistent, the presented expression for the change in the variance components estimator asymptotically holds for the maximum likelihood estimator as well. The results are illustrated with an analysis of mathematics performance data.

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