On the estimation of Bell regression model using ridge estimator

Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study were carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

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Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

F1000Research ◽

10.12688/f1000research.53987.2 ◽

2021 ◽

Vol 10 ◽

pp. 548

Author(s):

Benedicta B. Aladeitan ◽

Olukayode Adebimpe ◽

Adewale F. Lukman ◽

Olajumoke Oludoun ◽

Oluwakemi E. Abiodun

Keyword(s):

Regression Model ◽

Poisson Regression ◽

Generalized Linear Model ◽

Real Life ◽

Poisson Regression Model ◽

Likelihood Estimator ◽

Ridge Estimator ◽

Liu Estimator ◽

Life Study ◽

Ridge Regression Estimator

Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study was carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

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Preliminary test almost unbiased ridge estimator in a linear regression model with multivariate Student-t errors

Acta et Commentationes Universitatis Tartuensis de Mathematica ◽

10.12697/acutm.2011.15.03 ◽

2020 ◽

Vol 15 (1) ◽

pp. 27-43

Author(s):

Jianwen Xu ◽

Hu Yang

Keyword(s):

Regression Model ◽

Sufficient Conditions ◽

Preliminary Test ◽

Multiple Regression Model ◽

Regression Coefficients ◽

Lagrangian Multiplier ◽

Ridge Estimator ◽

Lm Tests ◽

Theoretical Results ◽

Almost Unbiased

In this paper, the preliminary test almost unbiased ridge estimators of the regression coefficients based on the conflicting Wald (W), Likelihood ratio (LR) and Lagrangian multiplier (LM) tests in a multiple regression model with multivariate Student-t errors are introduced when it is suspected that the regression coefficients may be restricted to a subspace. The bias and quadratic risks of the proposed estimators are derived and compared. Sufficient conditions on the departure parameter ∆ and the ridge parameter k are derived for the proposed estimators to be superior to the almost unbiased ridge estimator, restricted almost unbiased ridge estimator and preliminary test estimator. Furthermore, some graphical results are provided to illustrate theoretical results.

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Almost unbiased ridge estimator in the gamma regression model

Communications in Statistics - Simulation and Computation ◽

10.1080/03610918.2020.1722837 ◽

2020 ◽

pp. 1-21 ◽

Cited By ~ 3

Author(s):

Muhammad Amin ◽

Muhammad Qasim ◽

Ahad Yasin ◽

Muhammad Amanullah

Keyword(s):

Regression Model ◽

Ridge Estimator ◽

Almost Unbiased

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Stochastic Restricted Biased Estimators in Misspecified Regression Model with Incomplete Prior Information

Journal of Probability and Statistics ◽

10.1155/2018/1452181 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Manickavasagar Kayanan ◽

Pushpakanthie Wijekoon

Keyword(s):

Regression Model ◽

Prior Information ◽

Ridge Estimator ◽

Monte Carlo Simulation Study ◽

Error Matrix ◽

Liu Estimator ◽

Explanatory Variables ◽

Biased Estimators ◽

Incomplete Prior Information ◽

Almost Unbiased

The analysis of misspecification was extended to the recently introduced stochastic restricted biased estimators when multicollinearity exists among the explanatory variables. The Stochastic Restricted Ridge Estimator (SRRE), Stochastic Restricted Almost Unbiased Ridge Estimator (SRAURE), Stochastic Restricted Liu Estimator (SRLE), Stochastic Restricted Almost Unbiased Liu Estimator (SRAULE), Stochastic Restricted Principal Component Regression Estimator (SRPCRE), Stochastic Restricted r-k (SRrk) class estimator, and Stochastic Restricted r-d (SRrd) class estimator were examined in the misspecified regression model due to missing relevant explanatory variables when incomplete prior information of the regression coefficients is available. Further, the superiority conditions between estimators and their respective predictors were obtained in the mean square error matrix (MSEM) sense. Finally, a numerical example and a Monte Carlo simulation study were used to illustrate the theoretical findings.

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