Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression

Akdeniz, Fikri; Erol, Hamza

doi:10.1081/sta-120025385

Cited by 117 publications

(65 citation statements)

References 15 publications

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“…It is easily seen from (4) and (12) thatγ (D) andγ JGLE (D) are always biased estimators of γ . Akdeniz and Erol (2003) defined the variances of the GLE and JGLE as…”

Section: The Model Gle and Jglementioning

confidence: 99%

Efficiency of the modified jackknifed Liu-type estimator

Duran

Akdeniz

2010

Stat Papers

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In this article, we proposed a new estimator namely, modified jackknifed generalized Liu-type estimator (MJGLE). It is based on the criterion that it combines the ideas underlying both the generalized Liu estimator (GLE) and jackknifed generalized Liu estimator (JGLE). The performance of this estimator (MJGLE) is compared to that of the GLE and the JGLE. The ideas in the article are illustrated and evaluated using a real data example and simulations.

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“…It is easily seen from (4) and (12) thatγ (D) andγ JGLE (D) are always biased estimators of γ . Akdeniz and Erol (2003) defined the variances of the GLE and JGLE as…”

Section: The Model Gle and Jglementioning

confidence: 99%

Efficiency of the modified jackknifed Liu-type estimator

Duran

Akdeniz

2010

Stat Papers

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“…Sakallıoǧlu et al (2001) have dealt with the comparisons among the RE, Liu estimator and iteration estimator constructed as alternatives to the LSE when multicollinearity is present. Akdeniz and Erol (2003) have compared the almost unbiased generalized ridge estimator with the almost unbiased generalized Liu estimator in the mean squared error matrix (MSEM) sense. Sakallıooǧlu and Kaçıranlar (2008) have obtained a new biased estimator and compared it with the LSE, Liu estimator, and two Liu-type estimators.…”

Section: Introductionmentioning

confidence: 99%

A new Liu-type estimator in linear regression model

Yang

2010

Stat Papers

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In this paper, we introduce a new Liu-type estimator called modified Liu estimator based on prior information for the vector of parameters in a linear regression model and discuss its properties. Furthermore, we obtain that our new estimator is superior, in the mean square error matrix sense, to the least squares estimator, Liu estimator, ridge estimator and modified ridge estimator. Finally, a numerical example and a Monte Carlo simulation are done to illustrate some of the theoretical results.

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“…The data was discussed in Gruber [19], and the data has been analysed by Akdeniz and Erol [20], Li and Yang [21] and among others. Now we assemble the data as fol- Table 2, it can be observed that the predictors behave differently than the respective estimators, which is also agreed with our theoretical findings.…”

Section: Numerical Examplementioning

confidence: 99%

Performance of Existing Biased Estimators and the Respective Predictors in a Misspecified Linear Regression Model

Kayanan¹,

Wijekoon²

2017

OJS

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In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression model when there exists multicollinearity among explanatory variables. A generalized form was used to compare these estimators and predictors in the mean square error sense. Further, theoretical findings were established using mean square error matrix and scalar mean square error. Finally, a numerical example and a Monte Carlo simulation study were done to illustrate the theoretical findings. The simulation study revealed that LE and RE outperform the other estimators when weak multicollinearity exists, and RE, r-k class and r-d class estimators outperform the other estimators when moderated and high multicollinearity exist for certain values of shrinkage parameters, respectively. The predictors based on the LE and RE are always superior to the other predictors for certain values of shrinkage parameters.

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Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression

Cited by 117 publications

References 15 publications

Efficiency of the modified jackknifed Liu-type estimator

Efficiency of the modified jackknifed Liu-type estimator

A new Liu-type estimator in linear regression model

Performance of Existing Biased Estimators and the Respective Predictors in a Misspecified Linear Regression Model

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