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Journal articles on the topic 'Liu Estimator'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

Amin, Muhammad, Hajra Ashraf, Hassan S. Bakouch, and Najla Qarmalah. "James Stein Estimator for the Beta Regression Model with Application to Heat-Treating Test and Body Fat Datasets." Axioms 12, no. 6 (2023): 526. http://dx.doi.org/10.3390/axioms12060526.

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The beta regression model (BRM) is used when the dependent variable may take continuous values and be bounded in the interval (0, 1), such as rates, proportions, percentages and fractions. Generally, the parameters of the BRM are estimated by the method of maximum likelihood estimation (MLE). However, the MLE does not offer accurate and reliable estimates when the explanatory variables in the BRM are correlated. To solve this problem, the ridge and Liu estimators for the BRM were proposed by different authors. In the current study, the James Stein Estimator (JSE) for the BRM is proposed. The m

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2

Li, Jing, and Xueyan Li. "Liu Estimator in Semiparametric Partially Linear Varying Coefficient Models." International Journal of Statistics and Probability 8, no. 6 (2019): 69. http://dx.doi.org/10.5539/ijsp.v8n6p69.

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This paper considers biased estimation for partially linear varying coefficient model to overcome the problem of multicollinearity. By the Liu estimation approach, we construct a profile Liu estimator for the constant coefficients. Furthermore, a restricted profile-Liu estimator is proposed for the situation that some additional linear restrictions are available. The properties of the proposed estimators are investigated.

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3

Omara, Tarek. "Robust Liu-Type Estimator for SUR Model." Statistics, Optimization & Information Computing 9, no. 3 (2021): 607–17. http://dx.doi.org/10.19139/soic-2310-5070-985.

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The Liu-type estimator is one of the shrink estimators that is used to remedy for a problem of multicollinearityin SUR model, but it is sensitive to the outlier. In this paper, we introduce the S Liu-type (SLiu-type) and MM Liu-type estimator (MMLiu-type) for SUR model. These estimators merge Liu-type estimator with S-estimator and with MM-estimator which makes it have high robustness at the different level of efficiency and at the same time prevents the bad effects of multicollinearity. Moreover, to get more robust features, we have modified the Liu-type estimator by making it depend on MM es

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4

Wu, Jibo. "The Mixed Liu Estimator in Stochastic Restricted Linear Measurement Error Model." Journal of Mathematics 2021 (January 28, 2021): 1–8. http://dx.doi.org/10.1155/2021/6624923.

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Ghapani and Babdi [1] proposed a mixed Liu estimator in linear measurement error model with stochastic linear restrictions. In this article, we propose an alternative mixed Liu estimator in the linear measurement error model with stochastic linear restrictions. The performance of the new mixed Liu estimator over the mixed estimator, Liu estimator, and mixed Liu estimator proposed by Ghapani and Babdi [1] are discussed in the sense of mean squared error matrix. Finally, a simulation study is given to show the performance of these estimators.

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5

Erdugan, Funda. "Shifted Liu-Type Estimator in The Linear Regression." Jurnal Matematika, Statistika dan Komputasi 19, no. 1 (2022): 195–209. http://dx.doi.org/10.20956/j.v19i1.21136.

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The methods to solve the problem of multicollinearity have an important issue in the linear regression. The Liu-type estimator is one of these methods used to reduce its effect. This estimator is an estimator with two parameters denoted and . Kurnaz and Akay (2015) [6] introduced a new approach for the Liu-type estimator and called it new Liu-type (NL) estimator. This proposed estimator is based on a continuous function of rather than two parameters and includes OLS, ridge estimator, Liu estimator, and some estimators with two biasing parameters as special cases. This study aimed to improve th

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6

Idowu, Janet Iyabo, Akin Soga Fasoranbaku, and Kayode Ayinde. "A two-parameter estimator for correlated regressors in gamma regression model." Science World Journal 18, no. 4 (2024): 590–96. http://dx.doi.org/10.4314/swj.v18i4.8.

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Gamma Modified Two Parameter (GMTP) is a novel biased two-parameter estimator proposed to address the effects of multicollinearity in Generalized Linear Models (GLMs). An expansion of the linear regression model's Modified Two Parameters (MTP) is the newly suggested estimator. The performance of the GMTP estimator over the maximum likelihood estimator (MLE), gamma ridge estimator (GRE), gamma Liu estimator (GLE), and gamma Liu-type estimator (GLTE) reviewed in this article are theoretically compared, and the estimator's properties is discussed. A simulation study that examine the effects of th

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7

Attah, Omokova M., and Samuel Olayemi Olanrewaju. "Efficient Combined Estimator for Parameter Estimation of Linear Regression Model with Multicollinearity." Asian Journal of Probability and Statistics 27, no. 5 (2025): 1–11. https://doi.org/10.9734/ajpas/2025/v27i5750.

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The classical linear regression model relies on several key assumptions, including homoscedasticity, normality of errors, independence of observations and the absence of multicollinearity among explanatory variables (Gujarati, 2021), These assumptions are rarely fulfilled in real life situations. Multicollinearity occurs when the assumption of independent explanatory variables is violated (Alreshidi et al., 2025), There are many sources of multicollinearity, some of which are the data collection methods, the constraints placed on the model or having an overdetermined model (Paul, 2006), When m

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8

Safitri, Margeliza, Netti Herawati, Bernadhita Herindri Samodera Utami, and Subian Saidi. "Simulation Study of Modified Two-Parameter Liu Estimator (MTPLE) Method to Overcome Multicollinearity in The Poisson Regression Model." International Journal of Scientific Research and Modern Technology 4, no. 2 (2025): 20–25. https://doi.org/10.5281/zenodo.14916371.

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This study aims to evaluate the performance of the Modified Two-Parameter Liu Estimator method in dealing with multicollinearity and compare the performance of Maximum Likelihood Estimator, Liu Estimator, and Modified Two-Parameter Liu Estimator. Simulated data was used with n = 30, 50, 75, 150, and 300 in a Poisson regression model (p = 4, 6, 8) with ρ = 0.89, 0.95, and 0.99. The performance is evaluated using the mean square error criterion. The study results showed the superiority of Modified Two-Parameter Liu Estimator over the other estimators as it has the smallest mean square error

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9

Alrweili, Hleil. "Liu-Type Estimator for the Poisson-Inverse Gaussian Regression Model: Simulation and Practical Applications." Statistics, Optimization & Information Computing 12, no. 4 (2024): 982–1003. http://dx.doi.org/10.19139/soic-2310-5070-1991.

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The Poisson-Inverse Gaussian regression model (PIGRM) is commonly used to analyze count datasets with over-dispersion. While the maximum likelihood estimator (MLE) is a standard choice for estimating PIGRM parameters, its performance may be suboptimal in the presence of correlated explanatory variables. To overcome this limitation, we introduce a novel Liu-type estimator for PIGRM. Our analysis includes an examination of the matrix mean square error (MMSE) and scalar mean square error (SMSE) properties of the proposed estimator, comparing them with those of the MLE, ridge, and Liu estimators.

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10

Abdelwahab, Mahmoud M., Mohamed R. Abonazel, Ali T. Hammad, and Amera M. El-Masry. "Modified Two-Parameter Liu Estimator for Addressing Multicollinearity in the Poisson Regression Model." Axioms 13, no. 1 (2024): 46. http://dx.doi.org/10.3390/axioms13010046.

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This study introduces a new two-parameter Liu estimator (PMTPLE) for addressing the multicollinearity problem in the Poisson regression model (PRM). The estimation of the PRM is traditionally accomplished through the Poisson maximum likelihood estimator (PMLE). However, when the explanatory variables are correlated, thus leading to multicollinearity, the variance or standard error of the PMLE is inflated. To address this issue, several alternative estimators have been introduced, including the Poisson ridge regression estimator (PRRE), Liu estimator (PLE), and adjusted Liu estimator (PALE), ea

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11

Lukman, Adewale F., B. M. Golam Kibria, Kayode Ayinde, and Segun L. Jegede. "Modified One-Parameter Liu Estimator for the Linear Regression Model." Modelling and Simulation in Engineering 2020 (August 19, 2020): 1–17. http://dx.doi.org/10.1155/2020/9574304.

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Motivated by the ridge regression (Hoerl and Kennard, 1970) and Liu (1993) estimators, this paper proposes a modified Liu estimator to solve the multicollinearity problem for the linear regression model. This modification places this estimator in the class of the ridge and Liu estimators with a single biasing parameter. Theoretical comparisons, real-life application, and simulation results show that it consistently dominates the usual Liu estimator. Under some conditions, it performs better than the ridge regression estimators in the smaller MSE sense. Two real-life data are analyzed to illust

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12

Dai, Dayang, and Dabuxilatu Wang. "A generalized Liu-type estimator for logistic partial linear regression model with multicollinearity." AIMS Mathematics 8, no. 5 (2023): 11851–74. http://dx.doi.org/10.3934/math.2023600.

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<abstract><p>This paper is concerned with proposing a generalized Liu-type estimator (GLTE) to address the multicollinearity problem of explanatory variable of the linear part in the logistic partially linear regression model. Using the profile likelihood method, we propose the GLTE as a general class of Liu-type estimator, which includes the profile likelihood estimator, the ridge estimator, the Liu estimator and the Liu-type estimator as special cases. The conditional superiority of the proposed GLTE over the other estimators is derived under the asymptotic mean square error matr

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13

SÖKÜT AÇAR, Tuğba. "Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation." Journal of New Theory, no. 41 (December 31, 2022): 1–17. http://dx.doi.org/10.53570/jnt.1139885.

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The sensitivity of the least-squares estimation in a regression model is impacted by multicollinearity and autocorrelation problems. To deal with the multicollinearity, Ridge, Liu, and Ridge-type biased estimators have been presented in the statistical literature. The recently proposed Kibria-Lukman estimator is one of the Ridge-type estimators. The literature has compared the Kibria-Lukman estimator with the others using the mean square error criterion for the linear regression model. It was achieved in a study conducted on the Kibria-Lukman estimator's performance under the first-order autor

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14

Omara, Tarek. "Robust Lasso Estimator for the Liu-Type regression model and its applications." Statistics, Optimization & Information Computing 13, no. 5 (2025): 1819–31. https://doi.org/10.19139/soic-2310-5070-2106.

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In this paper, we propose a new estimator for Liu-Type regression model, called the LAD-Lasso-Liu estimator, which addresses the issues of multicollinearity, outliers and it performs the variable selection. By combining the LAD Lasso and Liu-Type estimators, our proposed estimator achieves double shrinkage for the parameters and at the same time it has the robust properties. We thoroughly discuss the properties of the new estimator and conduct a simulation study to demonstrate its superiority over the LAD, Lasso, and LAD-Lasso estimators. We used the Median(MSE) as a criteria to compare betwee

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15

Mohammed, M. A., Huda M. Alshanbari, and Abdal-Aziz H. El-Bagoury. "Application of the LINEX Loss Function with a Fundamental Derivation of Liu Estimator." Computational Intelligence and Neuroscience 2022 (March 14, 2022): 1–9. http://dx.doi.org/10.1155/2022/2307911.

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For a variety of well-known approaches, optimum predictors and estimators are determined in relation to the asymmetrical LINEX loss function. The applications of an iteratively practicable lowest mean squared error estimation of the regression disturbance variation with the LINEX loss function are discussed in this research. This loss is a symmetrical generalisation of the quadratic loss function. Whenever the LINEX loss function is applied, we additionally look at the risk performance of the feasible virtually unbiased generalised Liu estimator and practicable generalised Liu estimator. Whene

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16

Araveeporn, Autcha. "Modified Liu Parameters for Scaling Options of the Multiple Regression Model with Multicollinearity Problem." Mathematics 12, no. 19 (2024): 3139. http://dx.doi.org/10.3390/math12193139.

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The multiple regression model statistical technique is employed to analyze the relationship between the dependent variable and several independent variables. The multicollinearity problem is one of the issues affecting the multiple regression model, occurring in regard to the relationship among independent variables. The ordinal least square is the standard method to evaluate parameters in the regression model, but the multicollinearity problem affects the unstable estimator. Liu regression is proposed to approximate the Liu estimators based on the Liu parameter, to overcome multicollinearity.

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17

Wu, Jibo. "Improved Liu-Type Estimator of Parameters in Two Seemingly Unrelated Regressions." ISRN Applied Mathematics 2014 (March 16, 2014): 1–6. http://dx.doi.org/10.1155/2014/679835.

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We consider the parameter estimation in two seemingly unrelated regression systems. To overcome the multicollinearity, we propose a Liu-type estimator in seemingly unrelated regression systems. The superiority of the new estimator over the classic estimator in the mean square error is discussed and we also discuss the admissibility of the Liu-type estimator.

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18

Kayanan, Manickavasagar, and Pushpakanthie Wijekoon. "Improved LARS Algorithm for Adaptive LASSO in the Linear Regression Model." Asian Journal of Probability and Statistics 26, no. 7 (2024): 86–95. http://dx.doi.org/10.9734/ajpas/2024/v26i7632.

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The adaptive LASSO method has been employed for reliable variable selection as an alternative to LASSO in linear regression models. This paper introduces an adjusted LARS algorithm that integrates adaptive LASSO with several biased estimators, including the 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. The effectiveness of the proposed algorithm is evaluated through Monte Carlo simulation and empirical examples.

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19

HUANG, J. W., L. MA, and R. LI. "STUDY ON MEASUREMENT RELIABILITY BASED ON LIU ESTIMATOR." Latin American Applied Research - An international journal 48, no. 3 (2018): 187–92. http://dx.doi.org/10.52292/j.laar.2018.224.

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In this paper, we introduce the Liu estimator in the measurement process as an alternative method to the ordinary least squares estimator. To compare the Liu estimator and the ordinary least squares estimator under the reliability criterion, a simulation study is conducted. Simulation study results show that Liu estimator is an effective method to replace OLS estimator in process measurement. When the Liu parameter choose in a reasonable range, Liu estimator superior to ordinary least squares estimator in terms of reliability.

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20

Tgarshan, Ramajeyam, and Pushpakanthie Wijekoon. "On a Mixed Poisson Liu Regression Estimator for Overdispersed and Multicollinear Count Data." Scientific World Journal 2022 (July 20, 2022): 1–18. http://dx.doi.org/10.1155/2022/8171461.

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The mixed Poisson regression models are commonly employed to analyze the overdispersed count data. However, multicollinearity is a common issue when estimating the regression coefficients by using the maximum likelihood estimator (MLE) in such regression models. To deal with the multicollinearity, a Liu estimator was proposed by Liu (1993). The Poisson-Modification of the Quasi Lindley (PMQL) regression model is a mixed Poisson regression model introduced recently. The primary interest of this paper is to introduce the Liu estimator for the PMQL regression model to mitigate the multicollineari

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21

Awwad, Fuad A., Kehinde A. Odeniyi, Issam Dawoud, et al. "New Two-Parameter Estimators for the Logistic Regression Model with Multicollinearity." WSEAS TRANSACTIONS ON MATHEMATICS 21 (June 16, 2022): 403–14. http://dx.doi.org/10.37394/23206.2022.21.48.

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We proposed new two-parameter estimators to solve the problem called multicollinearity for the logistic regression model in this paper. We have derived these estimators’ properties and using the mean squared error (MSE) criterion; we compare theoretically with some of existing estimators, namely the maximum likelihood, ridge, Liu estimator, Kibria-Lukman, and Huang estimators. Furthermore, we obtain the estimators for k and d. A simulation is conducted in order to compare the estimators' performances. For illustration purposes, two real-life applications have been analyzed, that supported both

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22

Wu, Jibo. "On the Performance of Principal Component Liu-Type Estimator under the Mean Square Error Criterion." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/858794.

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Wu (2013) proposed an estimator, principal component Liu-type estimator, to overcome multicollinearity. This estimator is a general estimator which includes ordinary least squares estimator, principal component regression estimator, ridge estimator, Liu estimator, Liu-type estimator,r-kclass estimator, andr-dclass estimator. In this paper, firstly we use a new method to propose the principal component Liu-type estimator; then we study the superior of the new estimator by using the scalar mean squares error criterion. Finally, we give a numerical example to show the theoretical results.

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23

Abdulkareem Abdulazeez, Qamar, and Zakariya Yahya Algamal. "Employing particle swarm optimization algorithm for shrinkage parameter estimation in generalized Liu estimator." International Journal of Advanced Statistics and Probability 8, no. 1 (2020): 10. http://dx.doi.org/10.14419/ijasp.v8i1.30565.

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It is well-known that in the presence of multicollinearity, the Liu estimator is an alternative to the ordinary least square (OLS) estimator and the ridge estimator. Generalized Liu estimator (GLE) is a generalization of the Liu estimator. However, the efficiency of GLE depends on appropriately choosing the shrinkage parameter matrix which is involved in the GLE. In this paper, a particle swarm optimization method, which is a metaheuristic continuous algorithm, is proposed to estimate the shrinkage parameter matrix. The simulation study and real application results show the superior performanc

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Aladeitan, Benedicta B., Olukayode Adebimpe, Adewale F. Lukman, Olajumoke Oludoun, and Oluwakemi E. Abiodun. "Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation." F1000Research 10 (December 14, 2021): 548. http://dx.doi.org/10.12688/f1000research.53987.2.

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Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study was carried out and the performance of the new estimator was compared with some of t

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Aladeitan, Benedicta B., Olukayode Adebimpe, Adewale F. Lukman, Olajumoke Oludoun, and Oluwakemi E. Abiodun. "Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation." F1000Research 10 (July 8, 2021): 548. http://dx.doi.org/10.12688/f1000research.53987.1.

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Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study were carried out and the performance of the new estimator was compared with some of

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26

Inan, Deniz, and Birsen E. Erdogan. "Liu-Type Logistic Estimator." Communications in Statistics - Simulation and Computation 42, no. 7 (2013): 1578–86. http://dx.doi.org/10.1080/03610918.2012.667480.

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Hammad, Ali T., Eslam H. Hafez, Usman Shahzad, Elif Yıldırım, Ehab M. Almetwally, and B. M. Golam Kibria. "New Modified Liu Estimators to Handle the Multicollinearity in the Beta Regression Model: Simulation and Applications." Modern Journal of Statistics 1, no. 1 (2025): 58–79. https://doi.org/10.64389/mjs.2025.01111.

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The beta regression model (BRM) is widely used for analyzing bounded response variables, such as proportions, percentages. However, when multicollinearity exists among explanatory variables, the conventional maximum likelihood estimator (MLE) becomes unstable and inefficient. To address this issue, we propose new modified Liu estimators for the BRM, designed to enhance estimation accuracy in the presence of high multicollinearity among predictors. The proposed estimators extend the traditional Liu estimator by incorporating flexible biasing parameters, offering a more robust alternative to the

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28

Seifollahi, Solmaz, Hossein Bevrani, and Olayan Albalawi. "Reducing Bias in Beta Regression Models Using Jackknifed Liu-Type Estimators: Applications to Chemical Data." Journal of Mathematics 2024 (January 27, 2024): 1–12. http://dx.doi.org/10.1155/2024/6694880.

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In the field of chemical data modeling, it is common to encounter response variables that are constrained to the interval (0, 1). In such cases, the beta regression model is often a more suitable choice for modeling. However, like any regression model, collinearity can present a significant challenge. To address this issue, the Liu-type estimator has been used as an alternative to the maximum likelihood estimator, but it suffers from bias. In this paper, we introduce the Jackknifed Liu-type estimator and its modified version, which demonstrate improved bias reduction compared to the original L

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29

Kayanan, Manickavasagar, and Pushpakanthie Wijekoon. "Stochastic Restricted Biased Estimators in Misspecified Regression Model with Incomplete Prior Information." Journal of Probability and Statistics 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/1452181.

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The analysis of misspecification was extended to the recently introduced stochastic restricted biased estimators when multicollinearity exists among the explanatory variables. The Stochastic Restricted Ridge Estimator (SRRE), Stochastic Restricted Almost Unbiased Ridge Estimator (SRAURE), Stochastic Restricted Liu Estimator (SRLE), Stochastic Restricted Almost Unbiased Liu Estimator (SRAULE), Stochastic Restricted Principal Component Regression Estimator (SRPCRE), Stochastic Restricted r-k (SRrk) class estimator, and Stochastic Restricted r-d (SRrd) class estimator were examined in the misspec

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Lukman, Adewale F., B. M. Golam Kibria, Cosmas K. Nziku, Muhammad Amin, Emmanuel T. Adewuyi, and Rasha Farghali. "K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model." Mathematics 11, no. 2 (2023): 340. http://dx.doi.org/10.3390/math11020340.

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Multicollinearity negatively affects the efficiency of the maximum likelihood estimator (MLE) in both the linear and generalized linear models. The Kibria and Lukman estimator (KLE) was developed as an alternative to the MLE to handle multicollinearity for the linear regression model. In this study, we proposed the Logistic Kibria-Lukman estimator (LKLE) to handle multicollinearity for the logistic regression model. We theoretically established the superiority condition of this new estimator over the MLE, the logistic ridge estimator (LRE), the logistic Liu estimator (LLE), the logistic Liu-ty

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Altukhaes, W. B., M. Roozbeh, and N. A. Mohamed. "Feasible robust Liu estimator to combat outliers and multicollinearity effects in restricted semiparametric regression model." AIMS Mathematics 9, no. 11 (2024): 31581–606. http://dx.doi.org/10.3934/math.20241519.

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<p>Regression analysis frequently encounters two issues: multicollinearity among the explanatory variables, and the existence of outliers in the data set. Multicollinearity in the semiparametric regression model causes the variance of the ordinary least-squares estimator to become inflated. Furthermore, the existence of multicollinearity may lead to wide confidence intervals for the individual parameters and even produce estimates with wrong signs. On the other hand, as is often known, the ordinary least-squares estimator is extremely sensitive to outliers, and it may be completely corru

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Akram, Muhammad Nauman, Muhammad Amin, Faiza Sami, Adam Braima Mastor, Omer Mohamed Egeh, and Abdisalam Hassan Muse. "A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application." Journal of Mathematics 2022 (March 30, 2022): 1–12. http://dx.doi.org/10.1155/2022/3323955.

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Poisson regression is a popular tool for modeling count data and is applied in medical sciences, engineering and others. Real data, however, are often over or underdispersed, and we cannot apply the Poisson regression. To overcome this issue, we consider a regression model based on the Conway–Maxwell Poisson (COMP) distribution. Generally, the maximum likelihood estimator is used for the estimation of unknown parameters of the COMP regression model. However, in the existence of multicollinearity, the estimates become unstable due to its high variance and standard error. To solve the issue, a n

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Amin, Muhammad, Muhammad Nauman Akram, B. M. Golam Kibria, Huda M. Alshanbari, Nahid Fatima, and Ahmed Elhassanein. "On the Estimation of the Binary Response Model." Axioms 12, no. 2 (2023): 175. http://dx.doi.org/10.3390/axioms12020175.

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The binary logistic regression model (LRM) is practical in situations when the response variable (RV) is dichotomous. The maximum likelihood estimator (MLE) is generally considered to estimate the LRM parameters. However, in the presence of multicollinearity (MC), the MLE is not the correct choice due to its inflated standard deviation (SD) and standard errors (SE) of the estimates. To combat MC, commonly used biased estimators, i.e., the Ridge estimators (RE) and Liu estimators (LEs), are preferred. However, most of the time, the traditional LE attains a negative value for its Liu parameter (

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34

Månsson, Kristofer, B. M. Golam Kibria, and Ghazi Shukur. "A New Liu Type of Estimator for the Restricted SUR Estimator." Journal of Modern Applied Statistical Methods 18, no. 1 (2020): 2–11. http://dx.doi.org/10.22237/jmasm/1556669340.

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A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity.

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Altukhaes, Waleed B., Mahdi Roozbeh, and Nur A. Mohamed. "Robust Liu Estimator Used to Combat Some Challenges in Partially Linear Regression Model by Improving LTS Algorithm Using Semidefinite Programming." Mathematics 12, no. 17 (2024): 2787. http://dx.doi.org/10.3390/math12172787.

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Outliers are a common problem in applied statistics, together with multicollinearity. In this paper, robust Liu estimators are introduced into a partially linear model to combat the presence of multicollinearity and outlier challenges when the error terms are not independent and some linear constraints are assumed to hold in the parameter space. The Liu estimator is used to address the multicollinearity, while robust methods are used to handle the outlier problem. In the literature on the Liu methodology, obtaining the best value for the biased parameter plays an important role in model predic

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36

Arumairajan, Sivarasa, and Sinnarasa Kayathiri. "A new stochastic restricted two-parameter estimator in multiplelinear regression model." Vavuniya Journal of Science 1, no. 1 (2022): 38–47. http://dx.doi.org/10.4038/vjs.v1i1.6.

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In this paper, we proposed a biased estimator, a new stochastic restricted two-parameter estimator (NSRTPE), for the multiple linear regression model to tackle the multicollinearity problem when the stochastic restrictions are available. Necessary and sufficient conditions for the superiority of the proposed estimator over the ordinary least square estimator (OLSE), ridge estimator (RE), Liu estimator (LE), almost unbiased Liu estimator (AULE), modified new two-parameter estimator (MNTPE), mixed estimator (ME), stochastic restricted Liu estimator (SRLE) were derived in the mean square error ma

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Herawati, Netti, Eva Silviana, Khoirin Nisa, and Subian Saidi. "The effectiveness of Liu-Estimator in predicting poverty levels in Indonesia: Comparative study and application of simulation." Multidisciplinary Science Journal 7, no. 4 (2024): 2025187. http://dx.doi.org/10.31893/multiscience.2025187.

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Several logistic regression studies have frequently encountered problems where the data contains multicollinearity. This condition negatively impacts parameter estimation. The Least Absolute Shrinkage and Selection Operator (LASSO) and the Liu Estimator are methods that can be employed to eliminate multicollinearity among independent variables. The objective of this research is to evaluate the effectiveness of the Liu Estimator in removing multicollinearity compared to the Maximum Likelihood Estimator (MLE) and LASSO, using simulation data for sample sizes of n = 25, 50, and 75 in a binary log

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Thayaparan, Kayathiri, Kayanan Manickavasagar, and Pushpakanthie Wijekoon. "Stochastic Restricted Modified Mixed Logistic Estimator." Austrian Journal of Statistics 54, no. 4 (2025): 59–81. https://doi.org/10.17713/ajs.v54i4.2043.

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In this study, we introduce a new estimator named the Stochastic Restricted Modified Mixed Logistic Estimator (SRMMLE), which is specifically designed to handle multicollinearity within the framework of stochastic linear restrictions. Further, we enhance the SRMMLE by modifying its coefficients, resulting in four distinct variants: Stochastic Restricted Modified Mixed Logistic Estimator 1 (SRMMLE1), Stochastic Restricted Modified Mixed Logistic Estimator 2 (SRMMLE2), Stochastic Restricted Modified Mixed Logistic Estimator 3 (SRMMLE3), and Stochastic Restricted Modified Mixed Logistic Estimator

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Filzmoser, Peter, and Fatma Sevinç Kurnaz. "A robust Liu regression estimator." Communications in Statistics - Simulation and Computation 47, no. 2 (2017): 432–43. http://dx.doi.org/10.1080/03610918.2016.1271889.

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Abonazel, Mohamed R., and Rasha A. Farghali. "Liu-Type Multinomial Logistic Estimator." Sankhya B 81, no. 2 (2018): 203–25. http://dx.doi.org/10.1007/s13571-018-0171-4.

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Kurnaz, Fatma Sevinç, and Kadri Ulaş Akay. "A new Liu-type estimator." Statistical Papers 56, no. 2 (2014): 495–517. http://dx.doi.org/10.1007/s00362-014-0594-6.

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LI, R., F. LI, and J. W. HUANG. "THE PREDICTIVE PERFORMANCE EVALUATION AND NUMERICAL EXAMPLE STUDY FOR THE PRINCIPAL COMPONENT TWO-PARAMETERS ESTIMATOR." Latin American Applied Research - An international journal 48, no. 3 (2019): 181–86. http://dx.doi.org/10.52292/j.laar.2018.223.

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In this paper, detailed comparisons are given between those estimators that can be derived from the principal component two-parameter estimator such as the ordinary least squares estimator, the principal components regression estimator, the ridge regression estimator, the Liu estimator, the r-k estimator and the r-d estimator by the prediction mean square error criterion. In addition, conditions for the superiority of the principal component two-parameter estimator over the others are obtained. Furthermore, a numerical example study is conducted to compare these estimators under the prediction

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Dawoud, Issam, Fuad A. Awwad, Elsayed Tag Eldin, and Mohamed R. Abonazel. "New Robust Estimators for Handling Multicollinearity and Outliers in the Poisson Model: Methods, Simulation and Applications." Axioms 11, no. 11 (2022): 612. http://dx.doi.org/10.3390/axioms11110612.

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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 reg

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Badawaire, Abdulrasheed Bello, Kayode Ayinde, and S. O. Olanrewaju. "Development of a Robust Generalized Least Squares Liu Estimator to Address Some Basic Assumptions Violations in Linear Regression Model." Asian Journal of Probability and Statistics 27, no. 5 (2025): 12–31. https://doi.org/10.9734/ajpas/2025/v27i5751.

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The linear regression model's parameters are frequently estimated using the ordinary least squares (OLS) estimator. When certain assumptions are met, the OLS is regarded as the best linear unbiased estimator. Nonetheless, it was discovered that the conclusions were false in a large number of documented situations when multicollinearity, autocorrelation, and heavy-tail outliers in the residual were all present. In this paper, we have developed an estimator of the parameters of linear regression model that jointly handles autocorrelation, multicollinearity, and heavy tail errors. Combining the r

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Ayanlowo, Ayanlola E., Ifedayo D. Oladapo, Olugbenga Obadina, Peter Madu, N., and Odeyemi, A. Sunday. "Regression Estimators under Joint Multicollinearity and Autocorrelation Conditions: The Two-Stage Kibria-Lukman Estimator as an Enhanced Approach." International Journal of Development Mathematics (IJDM) 2, no. 1 (2025): 217–27. https://doi.org/10.62054/ijdm/0201.17.

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Multicollinearity among predictors and autocorrelation in residuals present significant challenges to the reliability and accuracy of linear regression models. These issues cause traditional Ordinary Least Squares (OLS) estimators to yield inflated variances and biased parameter estimates, ultimately leading to unreliable statistical inferences. To address these limitations, various biased estimators have been developed. This paper investigates the performance of several such estimators, including the Ridge, Liu, Kibria-Lukman (KL), and the newly proposed Two-Stage Kibria-Lukman (Two-Stage KL)

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Lukman, Adewale Folaranmi, Jeza Allohibi, Segun Light Jegede, Emmanuel Taiwo Adewuyi, Segun Oke, and Abdulmajeed Atiah Alharbi. "Kibria–Lukman-Type Estimator for Regularization and Variable Selection with Application to Cancer Data." Mathematics 11, no. 23 (2023): 4795. http://dx.doi.org/10.3390/math11234795.

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Following the idea presented with regard to the elastic-net and Liu-LASSO estimators, we proposed a new penalized estimator based on the Kibria–Lukman estimator with L1-norms to perform both regularization and variable selection. We defined the coordinate descent algorithm for the new estimator and compared its performance with those of some existing machine learning techniques, such as the least absolute shrinkage and selection operator (LASSO), the elastic-net, Liu-LASSO, the GO estimator and the ridge estimator, through simulation studies and real-life applications in terms of test mean squ

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Kibria, B. M. Golam, and Adewale F. Lukman. "A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications." Scientifica 2020 (April 28, 2020): 1–16. http://dx.doi.org/10.1155/2020/9758378.

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The ridge regression-type (Hoerl and Kennard, 1970) and Liu-type (Liu, 1993) estimators are consistently attractive shrinkage methods to reduce the effects of multicollinearity for both linear and nonlinear regression models. This paper proposes a new estimator to solve the multicollinearity problem for the linear regression model. Theory and simulation results show that, under some conditions, it performs better than both Liu and ridge regression estimators in the smaller MSE sense. Two real-life (chemical and economic) data are analyzed to illustrate the findings of the paper.

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Idowu, Janet Iyabo, Akin Soga Fasoranbaku, and Kayode Ayinde. "A New Modified Liu Ridge-Type Estimator for the Gamma Regression Model." International Journal of Research and Scientific Innovation X, no. XII (2024): 801–15. http://dx.doi.org/10.51244/ijrsi.2023.1012062.

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The Gamma Regression Model (GRM) is a special form of the generalized linear model (GLM), where the response variable is positively skewed and well fitted to the gamma distribution. The most popular technique for estimating GRM coefficients is maximum likelihood (ML) estimation. The ML estimation method performs better if there is no correlation between the explanatory variables. It is known that the variance of the maximum likelihood estimator of the gamma regression coefficients is impacted in situations when the explanatory variables are correlated. Based on Aslam and Ahmad’s Modified Liu-R

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IDOWU, Janet Iyabo, Olasunkanmi James OLADAPO, Abiola Timothy OWOLABİ, Kayode AYİNDE, and Oyinlade AKİNMOJU. "Combating Multicollinearity: A New Two-Parameter Approach." Nicel Bilimler Dergisi 5, no. 1 (2023): 1–31. http://dx.doi.org/10.51541/nicel.1084768.

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The ordinary least square (OLS) estimator is the Best Linear Unbiased Estimator (BLUE) when all linear regression model assumptions are valid. The OLS estimator, however, becomes inefficient in the presence of multicollinearity. To circumvent the problem of multicollinearity, various one and two-parameter estimators have been proposed. This paper a new two-parameter estimator called Liu-Kibria Lukman Estimator (LKL) estimator. The theoretical and simulation results show that the proposed estimator performs better than some existing estimators considered in this study under some conditions, usi

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Li, Yalian, and Hu Yang. "Two Classes of Almost Unbiased Type Principal Component Estimators in Linear Regression Model." Journal of Applied Mathematics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/639070.

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This paper is concerned with the parameter estimator in linear regression model. To overcome the multicollinearity problem, two new classes of estimators called the almost unbiased ridge-type principal component estimator (AURPCE) and the almost unbiased Liu-type principal component estimator (AULPCE) are proposed, respectively. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a Monte Carlo simulation study is given to illustrate the performance of the proposed estimators.

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