Efficiency of the modified jackknifed Liu-type estimator

Duran, Esra Akdeniz; Akdeniz, Fikri

doi:10.1007/s00362-010-0334-5

Cited by 24 publications

(6 citation statements)

References 20 publications

(16 reference statements)

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“…Following Akdeniz and Akdeniz, 26 subsequently, we modified Equation () by replacing

{\overset{α}{true}}^{normalPML}

with

{\overset{α}{true}}^{normalPKL}

, then the modified jackknife PKL becomes

{\overset{α}{true}}^{MJPKL} = [((), normalI goodbreak- {(2 k {(normalΛ goodbreak+ normalkI)}^{- 1})}^{2})] {\overset{α}{true}}^{normalPKL},

where

{\overset{α}{true}}^{normalPKL} = [I - 2 k {(normalΛ + normalkI)}^{- 1}] {\overset{α}{true}}^{normalPML} .

…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Modified jackknife Kibria–Lukman estimator for the Poisson regression model

Oranye

Ugwuowo

2021

Concurrency and Computation

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Poisson regression is one of the methods to analyze count data and, the regression parameters are usually estimated using the maximum likelihood (ML) method.However, the ML method is sensitive to multicollinearity. Multicollinearity occurs when there is linear dependency among the explanatory variables. Multicollinearity often leads to unstable maximum likelihood estimates. In this article, we developed modified jackknifed Poisson Kibria-Lukman (MJPKL) estimator to mitigate multicollinearity in the Poisson regression model. We theoretically compared the MJPKL estimator with some existing estimators and obtained the condition for the superiority of MJPKL. A simulation study and real-life application were conducted to compare the performance of the estimators. It is evident from the simulation and real-life results that the modified jackknifed Poisson K-L estimator (MJPKLE) gives better results than other estimators under some conditions. Finally, the MJPKL estimator reduces the bias of the PKL estimator and dominates every estimator considered in this article.

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“…Following Akdeniz and Akdeniz, 26 subsequently, we modified Equation () by replacing

{\overset{α}{true}}^{normalPML}

with

{\overset{α}{true}}^{normalPKL}

, then the modified jackknife PKL becomes

{\overset{α}{true}}^{MJPKL} = [((), normalI goodbreak- {(2 k {(normalΛ goodbreak+ normalkI)}^{- 1})}^{2})] {\overset{α}{true}}^{normalPKL},

where

{\overset{α}{true}}^{normalPKL} = [I - 2 k {(normalΛ + normalkI)}^{- 1}] {\overset{α}{true}}^{normalPML} .

…”

Section: Methodsmentioning

confidence: 99%

“…Following Akdeniz and Akdeniz, 26 subsequently, we modified Equation ( 21) by replacing αPML with αPKL , then the modified jackknife…”

Section: The Jackknife Poisson K-l Estimatormentioning

confidence: 99%

Modified jackknife Kibria–Lukman estimator for the Poisson regression model

Oranye

Ugwuowo

2021

Concurrency and Computation

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“…In the context of the linear regression model, Singh et al proposed the Jackknife procedure to alleviate the problem of bias in generalized ridge estimator. The theoretical and application of the jackknife estimator have been studied by several authors …”

Section: Statistical Methodologymentioning

confidence: 99%

Developing a ridge estimator for the gamma regression model

Algamal

2018

Journal of Chemometrics

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The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The gamma regression model is a very popular model in the application when the response variable is positively skewed. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the gamma regression coefficients. To address this problem, a gamma ridge regression model has been proposed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. Our Monte Carlo simulation results and the real data application suggest that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error.

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“…In addressing the problem of multicollinearity, one of the suggested approaches is the ridge regression (RR) approach, as introduced by Hoerl and Kenard (1970). However, while the RR is noted to have optimal properties that enable it to manage the presence of multicollinearity, its estimators are significantly biased (Akdeniz Duran & Akdeniz 2012;Batah, Ramanathan & Gore 2008). In attempting to address the issue of bias in the RR approach, Singh, Chaubey and Dwivedi (1986) suggested an almost unbiased ridge estimator based on the Jackknife technique.…”

Section: Introductionmentioning

confidence: 99%

A Remedial Measure of Multicollinearity in Multiple Linear Regression in the Presence of High Leverage Points

Saied Ismaeel,

Midi,

Taher Omar

2024

JSM

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The ordinary least squares (OLS) is the widely used method in multiple linear regression model due to tradition and its optimal properties. Nonetheless, in the presence of multicollinearity, the OLS method is inefficient because the standard errors of its estimates become inflated. Many methods have been proposed to remedy this problem that include the Jackknife Ridge Regression (JAK). However, the performance of JAK is poor when multicollinearity and high leverage points (HLPs) which are outlying observations in the X- direction are present in the data. As a solution to this problem, Robust Jackknife Ridge MM (RJMM) and Robust Jackknife Ridge GM2 (RJGM2) estimators are put forward. Nevertheless, they are still not very efficient because they suffer from long computational running time, some elements of biased and do not have bounded influence property. This paper proposes a robust Jackknife ridge regression that integrates a generalized M estimator and fast improvised Gt (GM-FIMGT) estimator, in its establishment. We name this method the robust Jackknife ridge regression based on GM-FIMGT, denoted as RJFIMGT. The numerical results show that the proposed RJFIMGT method was found to be the best method as it has the least values of RMSE and bias compared to other methods in this study.

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Efficiency of the modified jackknifed Liu-type estimator

Cited by 24 publications

References 20 publications

Modified jackknife Kibria–Lukman estimator for the Poisson regression model

Modified jackknife Kibria–Lukman estimator for the Poisson regression model

Developing a ridge estimator for the gamma regression model

A Remedial Measure of Multicollinearity in Multiple Linear Regression in the Presence of High Leverage Points

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