Robust modified jackknife ridge estimator for the Poisson regression model with multicollinearity and outliers

Arum, Kingsley Chinedu; Ugwuowo, Fidelis Ifeanyi; Oranye, Henrietta Ebele

doi:10.1016/j.sciaf.2022.e01386

Cited by 10 publications

(8 citation statements)

References 23 publications

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“…Finally, if outliers and multicollinearity problems occurred together in the PRM, we recommend that practitioners use the RPMKL and RPKL estimators to estimate the regression parameters of the model. For future work, we aim to develop new estimators to deal with both outliers and multicollinearity problems simultaneously in the PRM, such as the robust jackknife Liu, robust jackknife Kibria-Lukman, and robust jackknife modified Kibria-Lukman estimators as an extension to Abonazel and Dawoud [26] and Arum et al [27].…”

Section: Discussionmentioning

confidence: 99%

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New Robust Estimators for Handling Multicollinearity and Outliers in the Poisson Model: Methods, Simulation and Applications

Dawoud

Awwad

Eldin

et al. 2022

Axioms

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The Poisson maximum likelihood (PML) is used to estimate the coefficients of the Poisson regression model (PRM). Since the resulting estimators are sensitive to outliers, different studies have provided robust Poisson regression estimators to alleviate this problem. Additionally, the PML estimator is sensitive to multicollinearity. Therefore, several biased Poisson estimators have been provided to cope with this problem, such as the Poisson ridge estimator, Poisson Liu estimator, Poisson Kibria–Lukman estimator, and Poisson modified Kibria–Lukman estimator. Despite different Poisson biased regression estimators being proposed, there has been no analysis of the robust version of these estimators to deal with the two above-mentioned problems simultaneously, except for the robust Poisson ridge regression estimator, which we have extended by proposing three new robust Poisson one-parameter regression estimators, namely, the robust Poisson Liu (RPL), the robust Poisson Kibria–Lukman (RPKL), and the robust Poisson modified Kibria–Lukman (RPMKL). Theoretical comparisons and Monte Carlo simulations were conducted to show the proposed performance compared with the other estimators. The simulation results indicated that the proposed RPL, RPKL, and RPMKL estimators outperformed the other estimators in different scenarios, in cases where both problems existed. Finally, we analyzed two real datasets to confirm the results.

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Section: Discussionmentioning

confidence: 99%

“…To reduce the bias of the RPRR estimator, Abonazel and Dawoud [26] proposed the robust jackknife ridge estimator for the PRM. Furthermore, the robust modified jackknife ridge estimator for the PRM was provided by Arum et al [27].…”

Section: Robust Poisson Ridge Regression Estimatormentioning

confidence: 99%

New Robust Estimators for Handling Multicollinearity and Outliers in the Poisson Model: Methods, Simulation and Applications

Dawoud

Awwad

Eldin

et al. 2022

Axioms

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“…OLS minimizes

{‖y - Xβ‖}_{2}^{2}

subject to an L2 norm with respect to

bold-italicβ

but fails to give a unique estimate in high dimensional settings when p > n 21 . Another threat to the performance of OLS is multicollinearity, which surfaces as a result of the correlation or linear dependency among the predictors 22–27 . Biased estimators such as the ridge regression estimator, 28 the Liu estimator, 29 modified ridge‐type estimator, 30 the Kibria–Lukman (KL) estimator, 31 robust principle component (PC)‐ridge estimator, 24 JKL estimator, 22 and others were developed to account for multicollinearity problem in linear regression models.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Two‐step hybrid modeling for variable selection and estimation: An application to quantitative structure activity relationship study

Oranye,

Ugwuowo,

Arum

2023

Journal of Chemometrics

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In this study, we developed a simple technique for effective parameter estimation and prediction of the quantitative structure activity relationship studies using a two‐step procedure. The first step is to choose the important molecular descriptors using the random forest regression, and the second step is to optimally predict the biological activity of the selected chemical compounds using the following estimators: ridge regression, jackknife ridge, Liu regression, jackknife Liu, Kibria–Lukman, and jackknife Kibria–Lukman. We conducted a simulation study and a real‐life analysis with a quantitative structure–activity relationship (QSAR) data with 2540 descriptors after preprocessing. The optimal prediction is determined using the cross‐validation error. The estimator with minimum cross‐validation error is considered best. It is obvious that performing jackknife estimation after random forest selection is preferred.

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“…( 3.3 ), 10% and 20% contamination were added to the model. where h = 10 is added to inflate the response variable 36 , 37 . The ridge parameter k is obtained using the following equation: where , and r denotes the number of estimated parameter.…”

Section: Simulation Studymentioning

confidence: 99%

Robust-stein estimator for overcoming outliers and multicollinearity

Lukman

Farghali

Kibria

et al. 2023

Sci Rep

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Linear regression models with correlated regressors can negatively impact the performance of ordinary least squares estimators. The Stein and ridge estimators have been proposed as alternative techniques to improve estimation accuracy. However, both methods are non-robust to outliers. In previous studies, the M-estimator has been used in combination with the ridge estimator to address both correlated regressors and outliers. In this paper, we introduce the robust Stein estimator to address both issues simultaneously. Our simulation and application results demonstrate that the proposed technique performs favorably compared to existing methods.

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Robust modified jackknife ridge estimator for the Poisson regression model with multicollinearity and outliers

Cited by 10 publications

References 23 publications

New Robust Estimators for Handling Multicollinearity and Outliers in the Poisson Model: Methods, Simulation and Applications

New Robust Estimators for Handling Multicollinearity and Outliers in the Poisson Model: Methods, Simulation and Applications

Two‐step hybrid modeling for variable selection and estimation: An application to quantitative structure activity relationship study

Robust-stein estimator for overcoming outliers and multicollinearity

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