Almost unbiased ridge estimator in the gamma regression model

Amin, Muhammad; Qasim, Muhammad; Yasin, Ahad; Amanullah, M. Mohamed

doi:10.1080/03610918.2020.1722837

Cited by 19 publications

(11 citation statements)

References 26 publications

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“…The Poisson regression model has been applied to the aircraft damage dataset initially by Myers et al . (2012) and subsequently by other researchers such as Asar and Genc (2017) and Amin et al . (2020) among others.…”

Section: Real Life Applicationmentioning

confidence: 84%

“…(2020) among others. By following the Pearson chi-square goodness of fit test, Amin et al . (2020) was able to ascertain that the data fits a Poisson regression model.…”

Section: Real Life Applicationmentioning

confidence: 99%

“…The dataset provides some detail on two separate aircrafts: The McDonnell Douglas A-4 Skyhawk and the A-6 Grumman Itruder. The dependent variable denotes the number of locations with damage on the aircraft and this follows a Poisson distribution (Asar and Genc, 2017; Amin et al ., 2020 ). The data set has three explanatory variables, X 1 shows the type of aircraft which makes the outcome binary (A-4 is coded as 0 and A-6 is coded as 1).…”

Section: Real Life Applicationmentioning

confidence: 99%

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

et al. 2021

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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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Section: Real Life Applicationmentioning

confidence: 84%

“…(2020) among others. By following the Pearson chi-square goodness of fit test, Amin et al . (2020) was able to ascertain that the data fits a Poisson regression model.…”

Section: Real Life Applicationmentioning

confidence: 99%

Section: Real Life Applicationmentioning

confidence: 99%

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

et al. 2021

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“…This estimator was also well studied in the literature and generalized to some models which are members of GLMs ( [16], [11]). On the other hand, several estimators have been proposed for dealing with the issue of multicollinearity in gamma regression model [24,29,8,21,9,6,7,3].…”

Section: Introductionmentioning

confidence: 99%

A New Two-parameter Estimator for the Gamma Regression Model

ASAR¹,

Algamal

2022

Stat., optim. inf. comput.

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In this paper, we propose a new two-parameter biased estimator in gamma regression models when there is collinearity among the regressors. We investigate the mean squared error (MSE) properties of the newly proposed estimator. Moreover, we provide some theorems to compare the new estimators to the existing ones. We conduct a Monte Carlo simulation study to compare the estimators under different designs of collinearity in the sense of MSE. Moreover, we provide a real data application to show the usefulness of the new estimator.The simulations and real data results show that the proposed estimator beats other competitor estimators.

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“…Furthermore, Månsson (2012) suggested ridge estimators for the negative binomial regression model. Recently, Amin et al (2020a) and Algamal (2018a) proposed some ridge estimators and recommended best ridge estimator for the gamma RR. Algamal (2018b) presented an efficient estimation algorithm of biasing parameter of the ridge estimator.…”

Section: Introductionmentioning

confidence: 99%

New ridge estimators in the inverse Gaussian regression: Monte Carlo simulation and application to chemical data

Amin

Qasim

Afzal

et al. 2020

Communications in Statistics - Simulation and Computation

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In numerous application areas, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, the inverse Gaussian regression model (IGRM) is an effective approach in such scenarios. The problem of multicollinearity is very common in several application areas like chemometrics, biology, finance, and so forth. The effects of multicollinearity can be reduced using the ridge estimator. This research proposes new ridge estimators to address the issue of multicollinearity in the IGRM. The performance of the new estimators is compared with the maximum likelihood estimator and some other existing estimators. The mean square error is used as a performance evaluation criterion. A Monte Carlo simulation study is conducted to assess the performance of the new ridge estimators based on the minimum mean square error criterion. The Monte Carlo simulation results show that the performance of the proposed estimators is better than the available methods. The comparison of proposed ridge estimators is also evaluated using two real chemometrics applications. The results of Monte Carlo simulation and real applications confirmed the superiority of the proposed ridge estimators to other competitor methods.

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Almost unbiased ridge estimator in the gamma regression model

Cited by 19 publications

References 26 publications

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

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

A New Two-parameter Estimator for the Gamma Regression Model

New ridge estimators in the inverse Gaussian regression: Monte Carlo simulation and application to chemical data

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