On the James-Stein estimator for the poisson regression model

Amin, Muhammad; Akram, Muhammad Nauman; Amanullah, M. Mohamed

doi:10.1080/03610918.2020.1775851

Cited by 42 publications

(29 citation statements)

References 28 publications

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“…The response variable, y represents the number of locations with damage on the aircraft, which follows a Poisson distribution 19,21 . Amin et al 28 Table 7. From Table 7, we observed that all the coefficients have a similar sign.…”

Section: Real Life Applicationmentioning

confidence: 99%

“…The response variable, y represents the number of locations with damage on the aircraft, which follows a Poisson distribution 19 , 21 . Amin et al 28 examine if the model follows a Poisson regression model by adopting the Pearson chi-square goodness of fit test. The test confirms that the response variable is well fitted to the Poisson distribution with test statistic (p-value) is given as 6.89812 (0.07521).…”

Section: Real Life Applicationmentioning

confidence: 99%

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A new estimator for the multicollinear Poisson regression model: simulation and application

Lukman

Adewuyi

Månsson

et al. 2021

Sci Rep

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The maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators' performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.

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Section: Real Life Applicationmentioning

confidence: 99%

Section: Real Life Applicationmentioning

confidence: 99%

A new estimator for the multicollinear Poisson regression model: simulation and application

Lukman

Adewuyi

Månsson

et al. 2021

Sci Rep

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show abstract

“…e Liu estimator is an ace in this regard as it avoids the disadvantages of the ridge estimator [10], where the main advantage of the ridge is easy to use, and it can be written in the explicate and the objective formulas. In the literature, various studies are available for the PRM to overcome the presence of collinearity [7,[11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Influence Diagnostic Methods in the Poisson Regression Model with the Liu Estimator

Khan

Amanullah

Amin

et al. 2021

Computational Intelligence and Neuroscience

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There is a long history of interest in modeling Poisson regression in different fields of study. The focus of this work is on handling the issues that occur after modeling the count data. For the prediction and analysis of count data, it is valuable to study the factors that influence the performance of the model and the decision based on the analysis of that model. In regression analysis, multicollinearity and influential observations separately and jointly affect the model estimation and inferences. In this article, we focused on multicollinearity and influential observations simultaneously. To evaluate the reliability and quality of regression estimates and to overcome the problems in model fitting, we proposed new diagnostic methods based on Sherman–Morrison Woodbury (SMW) theorem to detect the influential observations using approximate deletion formulas for the Poisson regression model with the Liu estimator. A Monte Carlo method is done for the assessment of the proposed diagnostic methods. Real data are also considered for the evaluation of the proposed methods. Results show the superiority of the proposed diagnostic methods in detecting unusual observations in the presence of multicollinearity compared to the traditional maximum likelihood estimation method.

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“…In this paper, we aim to develop shrinkage estimators that are both minimax and capable of effective risk reduction over the usual estimator. Recent studies, in the context of shrinkage estimation, include Selahattin et al(2011), Amin et al(2020), Yuzba et al(2020). Tsukuma and Kubukawa(2015) address the problem of estimating the mean vector of a singular multivariate normal distribution with an unknown singular covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

On shrinkage estimators improving the James-Stein estimator under balanced loss function

Hamdaoui

Terbeche

Benkhaled

2021

Pak.j.stat.oper.res.

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In this paper, we are interested in estimating a multivariate normal mean under the balanced loss function using the shrinkage estimators deduced from the Maximum Likelihood Estimator (MLE). First, we consider a class of estimators containing the James-Stein estimator, we then show that any estimator of this class dominates the MLE, consequently it is minimax. Secondly, we deal with shrinkage estimators which are not only minimax but also dominate the James- Stein estimator.

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On the James-Stein estimator for the poisson regression model

Cited by 42 publications

References 28 publications

A new estimator for the multicollinear Poisson regression model: simulation and application

A new estimator for the multicollinear Poisson regression model: simulation and application

Influence Diagnostic Methods in the Poisson Regression Model with the Liu Estimator

On shrinkage estimators improving the James-Stein estimator under balanced loss function

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