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

Algamal, Zakariya Yahya; Lukman, Adewale F.; Abonazel, Mohamed R.; Awwad, Fuad A.

doi:10.1155/2022/9503460

Cited by 14 publications

(5 citation statements)

References 47 publications

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“…For example, Månsson [10] proposed the RR estimator for the NB model, Türkan and Özel [11] suggested the modified jackknifed RR estimator for the Poisson model, Kaçiranlar and Dawoud [12] introduced some ridge parameters for the Poisson model, Zaldivar [13] considered the performance of some RR estimators for the Poisson model, Rashad and Algamal [14] developed a new RR estimator, and Yehia [15] suggested the restricted RR estimator for the Poisson model. Algamal et al [16] introduced the ridge and Liu estimators for the zero-inflated bell regression model. Akram et al [17] introduced some new ridge parameters for the zero-inflated NB regression model.…”

Section: Figurementioning

confidence: 99%

Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation

Abonazel

Awwad²,

Eldin³

et al. 2023

Front. Appl. Math. Stat.

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The Conway–Maxwell–Poisson (COMP) model is defined as a flexible count regression model used for over- and under-dispersion cases. In regression analysis, when the explanatory variables are highly correlated, this means that there is a multicollinearity problem in the model. This problem increases the standard error of maximum likelihood estimates. To manage the multicollinearity effects in the COMP model, we proposed a new modified Liu estimator based on two shrinkage parameters (k, d). To assess the performance of the proposed estimator, the mean squared error (MSE) criterion is used. The theoretical comparison of the proposed estimator with the ridge, Liu, and modified one-parameter Liu estimators is made. The Monte Carlo simulation and real data application are employed to examine the efficiency of the proposed estimator and to compare it with the ridge, Liu, and modified one-parameter Liu estimators. The results showed the superiority of the proposed estimator as it has the smallest MSE value.

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Section: Figurementioning

confidence: 99%

Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation

Abonazel

Awwad²,

Eldin³

et al. 2023

Front. Appl. Math. Stat.

Self Cite

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“…For information on how to handle and resolve this issue in other regression models; see e.g. [19][20][21][22]. On the other hand, Figure 2 displays the histogram and boxplot for dependent variable in rail-trail dataset.…”

Section: Library("vtable") St(railtrail) # In Table or Using; Summary...mentioning

confidence: 99%

A Simple Introduction to Regression Modeling using R

Kamel

Abonazel

2023

Computational Journal of Mathematical and Statistical Sciences

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In statistical modeling, regression analysis is a group of statistical processes used in R programming and statistics to determine the relationship between dataset variables. It is a solid technique for determining the factors that affect an issue of interest. You can confidently establish which elements are most important, which ones can be ignored, and how these factors interact when you do a regression. It can be used to simulate the long-term link between variables and gauge how strongly the relationships between them are related. Regression analysis is typically used to ascertain the relationship between the dataset's dependent and independent variables. Generally, regression analysis is used to determine the relationship between the dependent and independent variables of the dataset. Understanding how dependent variables change when one of the independent variables changes while the other independent variables remain constant is made easier with the use of regression analysis. As a result, it is easier to create a regression model and forecast values in response to changes in one of the independent variables. Based on the categories of dependent variables, the quantity of independent variables, and the contour of the regression line. In this paper, we use the R programming language to present various empirical investigations in statistics and econometrics. We next consider problems involving modeling the relationship between response and explanatory variables for linear and non-liner regression models.

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“…Te maximum likelihood estimation (MLE) is commonly used for parameter estimation in BRMs, but if the independent variables are ill-conditioned, the results may be unsatisfactory. Te variable selection methods, such as adjusted R 2 [6] or the swarm optimization method [7], can help to deal with this issue. However, this issue often necessitates the use of biased estimators, such as Stein-type estimators [8], ridge estimators [9,10], modifed ridge-type estimators [11], Liu estimators [12,13], two-parameter estimators [14], Dawoud-Kibria estimators [15], and also Liu-type estimators [16,17] which is of particular interest in this paper.…”

Section: Introductionmentioning

confidence: 99%

Reducing Bias in Beta Regression Models Using Jackknifed Liu-Type Estimators: Applications to Chemical Data

Seifollahi,

Bevrani,

Albalawi

2024

Journal of Mathematics

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In the field of chemical data modeling, it is common to encounter response variables that are constrained to the interval (0, 1). In such cases, the beta regression model is often a more suitable choice for modeling. However, like any regression model, collinearity can present a significant challenge. To address this issue, the Liu-type estimator has been used as an alternative to the maximum likelihood estimator, but it suffers from bias. In this paper, we introduce the Jackknifed Liu-type estimator and its modified version, which demonstrate improved bias reduction compared to the original Liu-type estimator. We assess the theoretical and numerical performance of these estimators through Monte Carlo simulations and real-data examples from the field of chemistry. Our findings highlight the significant improvements offered by the proposed estimators in terms of accuracy and reliability.

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

Cited by 14 publications

References 47 publications

Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation

Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation

A Simple Introduction to Regression Modeling using R

Reducing Bias in Beta Regression Models Using Jackknifed Liu-Type Estimators: Applications to Chemical Data

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