A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations

Arashi, Mohammad; Norouzirad, Mina; Roozbeh, Mahdi; Khan, Naushad Mamode

doi:10.3390/math9233057

Cited by 6 publications

(3 citation statements)

References 14 publications

(13 reference statements)

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“…For future work, for example, one can study the highdimensional case in beta regression as an extension to Arashi et al [45] or provide a robust biased estimation of beta regression as an extension to Awwad et al [41] and Dawoud and Abonazel [40].…”

Section: Gasoline Yield Datamentioning

confidence: 99%

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application

Abonazel

Algamal

Awwad

et al. 2022

Front. Appl. Math. Stat.

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The beta regression is a widely known statistical model when the response (or the dependent) variable has the form of fractions or percentages. In most of the situations in beta regression, the explanatory variables are related to each other which is commonly known as the multicollinearity problem. It is well-known that the multicollinearity problem affects severely the variance of maximum likelihood (ML) estimates. In this article, we developed a new biased estimator (called a two-parameter estimator) for the beta regression model to handle this problem and decrease the variance of the estimation. The properties of the proposed estimator are derived. Furthermore, the performance of the proposed estimator is compared with the ML estimator and other common biased (ridge, Liu, and Liu-type) estimators depending on the mean squared error criterion by making a Monte Carlo simulation study and through two real data applications. The results of the simulation and applications indicated that the proposed estimator outperformed ML, ridge, Liu, and Liu-type estimators.

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Section: Gasoline Yield Datamentioning

confidence: 99%

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application

Abonazel

Algamal

Awwad

et al. 2022

Front. Appl. Math. Stat.

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“…In this study, we simulate using R software with the help of bellreg-package [1,16]. The predictors are generated in accordance to [7,8,9,17,18,19,20,21,22,23,24,25]:…”

Section: Simulation Studymentioning

confidence: 99%

Combating the Multicollinearity in Bell Regression Model: Simulation and Application

Shewa

Ugwuowo

2022

J. Nig. Soc. Phys. Sci.

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Poisson regression model has been popularly used to model count data. However, over-dispersion is a threat to the performance of the Poisson regression model. The Bell Regression Model (BRM) is an alternative means of modelling count data with over-dispersion. Conventionally, the parameters in BRM is popularly estimated using the Method of Maximum Likelihood (MML). Multicollinearity posed challenge on the efficiency of MML. In this study, we developed a new estimator to overcome the problem of multicollinearity. The theoretical, simulation and application results were in favor of this new method.

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“…They examined the asymptotic behavior of the estimators, and provided the proposed estimators’ superiority requirements for the biasing parameters, and supported their findings by numerical calculations. Arashi, M. et al [ 28 ] proposed the ridge estimator for high-dimensional multicollinear data. They proved the consistency and derived some asymptotic properties of the proposed estimators and applied it to simulation experiments and real data set.…”

Section: Introductionmentioning

confidence: 99%

Liu-type pretest and shrinkage estimation for the conditional autoregressive model

Al-Momani

2023

PLoS ONE

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Spatial regression models have recently received a lot of attention in a variety of fields to address the spatial autocorrelation effect. One important class of spatial models is the Conditional Autoregressive (CA). Theses models have been widely used to analyze spatial data in various areas, as geography, epidemiology, disease surveillance, civilian planning, mapping of poorness signals and others. In this article, we propose the Liu-type pretest, shrinkage and positive shrinkages estimators for the large-scale effect parameter vector of the CA regression model. The set of the proposed estimators are evaluated analytically via their asymptotic bias, quadratic bias, the asymptotic quadratic risks, and numerically via their relative mean squared errors. Our results demonstrate that the proposed estimators are more efficient than Liu-type estimator. To conclude this paper, we apply the proposed estimators to the Boston housing prices data, and applied a bootstrapping technique to evaluate the estimators based on their mean squared prediction error.

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A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations

Cited by 6 publications

References 14 publications

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application

Combating the Multicollinearity in Bell Regression Model: Simulation and Application

Liu-type pretest and shrinkage estimation for the conditional autoregressive model

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