On the performance of the Jackknifed Liu-type estimator in linear regression model

Yıldız, Nilgün

doi:10.1080/03610926.2017.1339087

Cited by 10 publications

(6 citation statements)

References 11 publications

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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%

“…The theoretical and application of the jackknife estimator have been studied by several authors. [12][13][14][15][16][17][18] In this section, the Jackknifed ridge estimator of the GR is introduced. Let Λ = diag (λ 1 , λ 2 , …, λ p ) and Q = (q 1 , q 2 , …, q p ) respectively be the matrices of eigenvalues and eigenvectors of the X T c WX matrix, such that…”

Section: Jackknifed Gamma Ridge Estimatormentioning

confidence: 99%

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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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Section: Statistical Methodologymentioning

confidence: 99%

Section: Jackknifed Gamma Ridge Estimatormentioning

confidence: 99%

Developing a ridge estimator for the gamma regression model

Algamal

2018

Journal of Chemometrics

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“…In linear regression model, Singh, et al [28] 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 [22,[29][30][31][32][33][34][35].…”

Section: Modified Jackknife Ridge Estimator In Bell Regression Modelmentioning

confidence: 99%

Modified Jackknifed Ridge Estimator in Bell Regression Model: Theory, Simulation and Applications

2023

ijcsm

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the response variable i yR  which follows the Bell distribution. Then, the density function of i y can be expressed as ABSTRACT:Regression analyses look at how the answer variable and one or more explanatory factors are related. When the explanatory variables are linearly dependent, it becomes practically difficult to model this relationship in real-world applications. Several shrinkage estimators are suggested traditionally to avoid this problem. When there is linear dependency between the explanatory variables, one of the most widely used estimate techniques is the ridge estimator. In this paper, we suggested a jackknifed variant of the ridge estimator to reduce biasedness for the Bell regression model. The simulation results demonstrated that the proposed method is able to effectively outperform other alternatives estimators in terms of mean squared error (MSE). Further, the application results, which are based on two datasets: aircraft data and mine fracture data showed that the suggested estimator improves the ridge estimator's performance in terms of MSE.

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“…In this section, Yıldız [15] propose a new estimator for γ. The proposed estimator is designated as the modified jackknifed Liu-type estimator (MJLTE) denoted bŷ γ MJLTE k; d ðÞ…”

Section: Our Novel Mjlte Estimatormentioning

confidence: 99%

A Study on the Comparison of the Effectiveness of the Jackknife Method in the Biased Estimators

Yıldız¹

2020

Statistical Methodologies

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In this study, we proposed an alternative biased estimator. The linear regression model might lead to ill-conditioned design matrices because of the multicollinearity and thus result in inadequacy of the ordinary least squares estimator (OLS). Scientists have developed alternative estimation techniques that would eradicate the instability in the estimates. Several biased estimators such as Stein estimator, the ordinary ridge regression (ORR) estimator, the principal components regression (PCR) estimator. Liu developed a Liu estimator (LE) by combining the Stein estimator with the ORR estimator. Since both ORR and LE depend on OLS estimator, multicollinearity affects them both. Therefore, the ORR and LE may give misleading information in the presence of multicollinearity. To overcome this problem, Liu introduced a new estimator, which is based on k and d biasing parameters, the authors worked on developing an estimator that would still have the valuable characteristics of the Liu-type estimator (LTE) but have a smaller bias. We are proposing a modified jackknife Liu-type estimator (MJLTE) that was created by combining the ideas underlying both the LTE and JLTE. Under mean square error matrix criteria, the MJLTE is superior to Liu-type estimator (LTE) and jackknifed Liu-type estimator (JLTE). Finally, a real data example and a Monte Carlo simulation are also given to illustrate theoretical results.

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On the performance of the Jackknifed Liu-type estimator in linear regression model

Cited by 10 publications

References 11 publications

Developing a ridge estimator for the gamma regression model

Developing a ridge estimator for the gamma regression model

Modified Jackknifed Ridge Estimator in Bell Regression Model: Theory, Simulation and Applications

A Study on the Comparison of the Effectiveness of the Jackknife Method in the Biased Estimators

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