Performance of some new Liu parameters for the linear regression model

Qasim, Muhammad; Amin, Muhammad; Omer, Talha

doi:10.1080/03610926.2019.1595654

Cited by 46 publications

(42 citation statements)

References 14 publications

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“…However, estimator result in biased for a specific value of d, it exhibits minimum mean squared error (MSE) than the OLSE. Qasim et al (2019a) proposed some shrinkage estimators to estimate the value of d. We were used the following best estimator that suggested by Qasim et al (2019a):…”

Section: Experimentmentioning

confidence: 99%

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Effect of Different‎ Biochemical Traits on Seed Cotton Yield: An Application of Liu Linear Regression

2020

THE JAPS

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This article aimed to study the associations among the biochemical traits and their effects on seed cotton yield using the regression analysis and to assess the alternative approach for reducing the impact of multicollinearity problem in estimating the regression coefficients. The field experiment was conducted where five explanatory variables (chlorophyll 'a', chlorophyll 'b', total chlorophyll, total soluble protein and total soluble sugar) and one dependent variable seed cotton yield were measured. The correlation matrix of showed that biochemical traits were significantly correlated. The multicollinearity problem among the biochemical traits was determined by condition index and correlation matrix. Using the least square regression analysis, the effects of biochemical traits on seed cotton yield were not satisfactory since least square regression model has high value of MSE (3352475), AIC (366.7) and inconsistent estimates of traits. The Liu regression analysis was efficient (MSE = 57212 and AIC = 363.8) and reliable in reducing the adverse effects of multicollinearity. The Liu regression results indicated that total chlorophyll and total soluble protein were contributed a significant (P ≤ 0.05) role in seed cotton yield. In contrast, ordinary least square regression analysis was showed insignificant (P > 0.05) effect of total chlorophyll on seed cotton yield.

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Section: Experimentmentioning

confidence: 99%

“…Since is the jth eigenvalues of the matrix and is known as the estimated residual variance. For more knowledge regarding Liu estimator in the LRM (see, e.g., Liu, 1993, Qasim et al 2019a. The is on average too long in the presence of multicollinearity.…”

Section: Experimentmentioning

confidence: 99%

Effect of Different‎ Biochemical Traits on Seed Cotton Yield: An Application of Liu Linear Regression

2020

THE JAPS

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“…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%

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

Qasim

Månsson

Kibria

2021

Journal of Statistical Computation and Simulation

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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.

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“…Alternatively, different researchers have proposed other estimators to solve multicollinearity in the LRM. Authors include Hoerl and Kennard, 13 Liu, 15 Akdeniz and Kaciranlar, 16 Kibria, 17 Kibria and Banik, 18 Sakallioglu and Kaciranlar, 19 Yang and Chang, 20 Wu and Yang, 21 Dorugade, 22 Lukman et al, 9,10 Qasim et al, 23 Ahmad and Aslam, 24 Kibria and Lukman, 25 Liu (2003) 26 . Multicollinearity is also a threat to the performance of the MLE in IGRM.…”

Section: Introductionmentioning

confidence: 99%

TheKLestimator for the inverse Gaussian regression model

Lukman

Algamal

Kibria

et al. 2021

Concurrency and Computation

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Multicollinearity poses an undesirable effect on the efficiency of the maximum likelihood estimator (MLE) in both Gaussian and non‐Gaussian regression models. The ridge and the Liu estimators have been developed as an alternative to the MLE. Both estimators possess smaller mean squared error (MSE) over the MLE. Recently, Kibria and Lukman developed KL estimator, which was found to outperform the ridge and the Liu estimators in the linear regression model. With this expectation, we developed the KL estimator for the inverse Gaussian regression model. We compare the proposed estimator's performance with some existing estimators in terms of theoretical comparison, the simulation study, and real‐life application. Smaller MSE criterion shows that the proposed estimator with one of its shrinkage parameter performs the best.

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Performance of some new Liu parameters for the linear regression model

Cited by 46 publications

References 14 publications

Effect of Different‎ Biochemical Traits on Seed Cotton Yield: An Application of Liu Linear Regression

Effect of Different‎ Biochemical Traits on Seed Cotton Yield: An Application of Liu Linear Regression

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

TheKLestimator for the inverse Gaussian regression model

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