Biased Adjusted Poisson Ridge Estimators-Method and Application

Qasim, Muhammad; Månsson, Kristofer; Amin, Muhammad; Kibria, B. M. Golam; Sjölander, Pär

doi:10.1007/s40995-020-00974-5

Cited by 17 publications

(14 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Following Månsson and Shukur 3 and Qasim et al, 8 we suggest the following biasing parameters for the PRR, RPRR, PAUR, and RPAUR estimators: The suggested

\hat{k}

for the PRR estimator is

{\hat{k}}_{PRR}=\max {\left(\sqrt{{\hat{\alpha}}_j^2}\right)}_{j=1}^{p+1}.

The suggested

\hat{k}

for the RPRR estimator is

$$ {\hat{k}}_{RPRR}=\max {\left(\sqrt{{\hat{\alpha}}_j^{\ast 2}}\right)}_{j=1}^{p+1}.

…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Developing robust ridge estimators for Poisson regression model

Abonazel

Dawoud

2022

Concurrency and Computation

View full text Add to dashboard Cite

The Poisson regression model (PRM) is the standard statistical method of analyzing count data, and it is estimated by a Poisson maximum likelihood (PML) estimator. Such an estimator is affected by outliers, and some robust Poisson regression estimators have been proposed to solve this problem. PML estimators are also influenced by multicollinearity. Biased Poisson regression estimators have been developed to address this problem, including Poisson ridge regression and Poisson almost unbiased ridge estimators. However, the above mentioned estimators do not deal with outliers and multicollinearity problems together in a PRM. Therefore, we propose two robust ridge estimators to deal with the two problems simultaneously in the PRM, namely, the robust Poisson ridge regression (RPRR) estimator and the robust Poisson almost unbiased ridge (RPAUR) estimator. Theoretical comparisons and Monte-Carlo simulations are conducted to investigate the performance of the proposed estimators relative to the performance of other approaches to PRM parameter estimation. The simulation results indicate that the RPAUR estimator outperforms the other estimators in all situations where both problems exist. Finally, real data are used to confirm the results of this paper. K E Y W O R D S mean squared error, Monte-Carlo simulations, multicollinearity, outliers, robust Poisson almost unbiased ridge regression estimator, robust Poisson ridge regression estimator 1 INTRODUCTION The Poisson regression model (PRM) is the most widely used model for analyzing count data. Poisson maximum likelihood (PML) estimators for PRMs are implemented via the iterative weighted least square (IWLS) algorithm. PML estimators are affected by outliers, and some researchers have provided robust estimators for PRMs to address this problem, such as Cantoni and Ronchetti 1 and Hosseinian and Morgenthaler. 2 However, when multicollinearity occurs among the explanatory variables in the PRM, the PML estimator cannot estimate unknown regression parameters well. Different biased estimators have been suggested to solve this problem in the PRM, such as the Poisson ridge regression (PRR) estimator, 3 the Poisson Liu estimator, 4 the Poisson ridge-type estimator, 5 and the Poisson modified ridge-type estimator. 6 Furthermore, the Poisson almost unbiased ridge (PAUR) estimator is introduced by Türkan and Özel. 7 The mean squared error (MSE) properties of these estimators have been examined. Moreover, authors have adopted and modified new approaches to estimating the biasing parameter k, which is given in many studies. For more details, see Månsson and Shukur, 3 Türkan and Özel, 7 and Qasim et al. 8The PRM is a popular model used for analyzing count data in cases where the distribution of the dependent variable (y i ) is Poisson (𝜇 i ) such that 𝜇 i (𝛽) = exp (x i 𝛽), where x i is the ith row of the X matrix (which is an n × (p + 1) data matrix with p number of explanatory variables), and 𝛽 is

show abstract

“…Following Månsson and Shukur 3 and Qasim et al, 8 we suggest the following biasing parameters for the PRR, RPRR, PAUR, and RPAUR estimators: The suggested

\hat{k}

for the PRR estimator is

{\hat{k}}_{PRR}=\max {\left(\sqrt{{\hat{\alpha}}_j^2}\right)}_{j=1}^{p+1}.

The suggested

\hat{k}

for the RPRR estimator is

$$ {\hat{k}}_{RPRR}=\max {\left(\sqrt{{\hat{\alpha}}_j^{\ast 2}}\right)}_{j=1}^{p+1}.

…”

Section: Methodsmentioning

confidence: 99%

“…Moreover, authors have adopted and modified new approaches to estimating the biasing parameter k , which is given in many studies. For more details, see Månsson and Shukur, 3 Türkan and Özel, 7 and Qasim et al 8 …”

Section: Introductionmentioning

confidence: 99%

Developing robust ridge estimators for Poisson regression model

Abonazel

Dawoud

2022

Concurrency and Computation

View full text Add to dashboard Cite

show abstract

“…There are several methods to estimate the shrinkage parameter (see, e.g. [16][17][18][19][20][21]). Unlike linear regression, the effect of multicollinearity on GLM has not significantly been discussed in the literature using ridge regression approach.…”

Section: Introductionmentioning

confidence: 99%

“…Exceptionally, Månsson and Shukur [22] introduced some ridge parameters for the logistic regression model, Månsson and Shukur [23] established a Poisson ridge regression (PRR) estimator. Since PRR can have a severe bias, Qasim et al [20] suggested bias adjusted PRR estimators. Amin et al [19] examined the performance of inverse Gaussian ridge regression estimators.…”

Section: Introductionmentioning

confidence: 99%

On some beta ridge regression estimators: method, simulation and application

Qasim

Månsson

Kibria

2021

Journal of Statistical Computation and Simulation

Self Cite

View full text Add to dashboard Cite

The classic statistical method for modelling the rates and proportions is the beta regression model (BRM). The standard maximum likelihood estimator (MLE) is used to estimate the coefficients of the BRM. However, this MLE is very sensitive when the regressors are linearly correlated. Therefore, this study introduces a new beta ridge regression (BRR) estimator as a remedy to the problem of instability of the MLE. We study the mean squared error properties of the BRR estimator analytically and then based on the derived MSE, we suggest some new estimators of the shrinkage parameter. We also suggest a median squared error (SE) performance criterion, which can be used to achieve strong evidence in favour of the proposed method for the Monte Carlo simulation study. The performance of BRR and MLE is appraised through Monte Carlo simulation. Finally, an empirical application is used to show the advantages of the proposed estimator.

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Biased Adjusted Poisson Ridge Estimators-Method and Application

Cited by 17 publications

References 14 publications

Developing robust ridge estimators for Poisson regression model

Developing robust ridge estimators for Poisson regression model

On some beta ridge regression estimators: method, simulation and application

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

Contact Info

Product

Resources

About