A New Ridge-Type Estimator for the Gamma Regression Model

Lukman, Adewale F.; Dawoud, İssam; Kibria, Golam; Algamal, Zakariya Yahya; Aladeitan, Benedicta

doi:10.1155/2021/5545356

Cited by 18 publications

(20 citation statements)

References 26 publications

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“…Very recently, Dawoud and Kibria [5] proposed a new kind of two-parameter estimator called the Dawoud-Kibria (DK) estimator. There are other recent studies regarding the one parameter and two-parameter estimators in LR and GL models, such as Roozbeh et al [6], Lukman et al [7], Arashi et al [8], Farghali et al [9], Lukman et al [10,11], Algamal and Abonazel [12], Akram et al [13], and Abonazel et al [14]. In this article, we drive the Dawoud-Kibria estimator for the BR model in the presence of the multicollinearity problem.…”

Section: Introductionmentioning

confidence: 90%

Dawoud–Kibria Estimator for Beta Regression Model: Simulation and Application

Abonazel

Dawoud

Awwad

et al. 2022

Front. Appl. Math. Stat.

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The linear regression model becomes unsuitable when the response variable is expressed as percentages, proportions, and rates. The beta regression (BR) model is more appropriate for the variable of this form. The BR model uses the conventional maximum likelihood estimator (BML), and this estimator may not be efficient when the regressors are linearly dependent. The beta ridge estimator was suggested as an alternative to BML in the literature. In this study, we developed the Dawoud–Kibria estimator to handle multicollinearity in the BR model. The properties of the new estimator are derived. We compared the performance of the estimator with the existing estimators theoretically using the mean squared error criterion. A Monte Carlo simulation and a real-life application were carried out to show the benefits of the proposed estimator. The theoretical comparison, simulation, and real-life application results revealed the superiority of the proposed estimator.

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Section: Introductionmentioning

confidence: 90%

Dawoud–Kibria Estimator for Beta Regression Model: Simulation and Application

Abonazel

Dawoud

Awwad

et al. 2022

Front. Appl. Math. Stat.

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“…In this section, we generated explanatory variables that are collinear and a response variable y that follows a zeroinflated bell distribution. e explanatory variables are obtained in line with the following studies [42][43][44][45][46][47][48]:…”

Section: Simulation Studymentioning

confidence: 99%

Performance of the Ridge and Liu Estimators in the zero‐inflated Bell Regression Model

Algamal

Lukman

Abonazel

et al. 2022

Journal of Mathematics

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The Poisson regression model is popularly used to model count data. However, the model suffers drawbacks when there is overdispersion—when the mean of the Poisson distribution is not the same as the variance. In this situation, the Bell regression model fits well to the data. Also, there is a high tendency of excess zeros in the count data. In this case, the zero-inflated Bell regression model is an alternative to the Bell regression model. The parameters of the zero-inflated Bell regression model are mostly estimated using the method of maximum likelihood. Linear dependency is a threat in a real-life application when modeling the relationship between the response variable and two or more explanatory variables in a generalized linear model such as the zero-inflated Bell regression model. It reduced the efficiency of the maximum likelihood estimator. Therefore, we developed the ridge and Liu estimators for the zero-inflated Bell regression model to deal with this issue. The simulation and application results support the dominance of the proposed methods over the conventional maximum likelihood estimator.

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“…Recently, Kibria and Lukman [9] proposed a new ridge-type estimator (NRTE). The NRTE has been extended in different regression models in different studies, such as Lukman et al [10], Lukman et al [11], Akram et al [12], Dawoud and Abonazel [13], Awwad et al [14], and Abonazel et al [15]. The multicollinearity is known to be a terrible problem in the Tobit model like in the LRM.…”

Section: Introductionmentioning

confidence: 99%

A New Tobit Ridge-Type Estimator of the Censored Regression Model With Multicollinearity Problem

Dawoud

Abonazel²,

Awwad³

et al. 2022

Front. Appl. Math. Stat.

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In the censored regression model, the Tobit maximum likelihood estimator is unstable and inefficient in the occurrence of the multicollinearity problem. To reduce this problem's effects, the Tobit ridge and the Tobit Liu estimators are proposed. Therefore, this study proposes a new kind of the Tobit estimation called the Tobit new ridge-type (TNRT) estimator. Also, the TNRT estimator was theoretically compared with the Tobit maximum likelihood, the Tobit ridge, and the Tobit Liu estimators via the mean squared error criterion. Moreover, we performed a Monte Carlo simulation to study the performance of the TNRT estimator compared with the previously defined estimators. Also, we used the Mroz dataset to confirm the theoretical and the simulation study results.

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A New Ridge-Type Estimator for the Gamma Regression Model

Cited by 18 publications

References 26 publications

Dawoud–Kibria Estimator for Beta Regression Model: Simulation and Application

Dawoud–Kibria Estimator for Beta Regression Model: Simulation and Application

Performance of the Ridge and Liu Estimators in the zero‐inflated Bell Regression Model

A New Tobit Ridge-Type Estimator of the Censored Regression Model With Multicollinearity Problem

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