Stochastic Restricted Biased Estimators in Misspecified Regression Model with Incomplete Prior Information

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 misspecified regression model due to missing relevant explanatory variables when incomplete prior information of the regression coefficients is available. Further, the superiority conditions between estimators and their respective predictors were obtained in the mean square error matrix (MSEM) sense. Finally, a numerical example and a Monte Carlo simulation study were used to illustrate the theoretical findings.

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Two Kinds of Weighted Biased Estimators in Stochastic Restricted Regression Model

Journal of Applied Mathematics ◽

10.1155/2014/314875 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Chaolin Liu ◽

Haina Jiang ◽

Xinhui Shi ◽

Donglin Liu

Keyword(s):

Monte Carlo ◽

Regression Model ◽

Prior Information ◽

Monte Carlo Study ◽

Real Data ◽

Variance Matrix ◽

Unbiased Estimators ◽

Biased Estimators ◽

Theoretical Results ◽

Almost Unbiased

We consider two kinds of weighted mixed almost unbiased estimators in a linear stochastic restricted regression model when the prior information and the sample information are not equally important. The superiorities of the two new estimators are discussed according to quadratic bias and variance matrix criteria. Under such criteria, we perform a real data example and a Monte Carlo study to illustrate theoretical results.

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Two Classes of Almost Unbiased Type Principal Component Estimators in Linear Regression Model

Journal of Applied Mathematics ◽

10.1155/2014/639070 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Yalian Li ◽

Hu Yang

Keyword(s):

Linear Regression ◽

Regression Model ◽

Linear Regression Model ◽

Mean Squared Error ◽

Principal Component ◽

Monte Carlo Simulation Study ◽

Error Matrix ◽

Squared Error ◽

The Mean ◽

Almost Unbiased

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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On the almost unbiased Ridge and Liu estimator in the Logistic regression model

Proceedings of the 2015 International Conference on Social Science, Education Management and Sports Education ◽

10.2991/ssemse-15.2015.424 ◽

2015 ◽

Author(s):

Xinfeng Chang

Keyword(s):

Logistic Regression ◽

Regression Model ◽

Logistic Regression Model ◽

Liu Estimator ◽

Almost Unbiased

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Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

F1000Research ◽

10.12688/f1000research.53987.1 ◽

2021 ◽

Vol 10 ◽

pp. 548

Author(s):

Benedicta B. Aladeitan ◽

Olukayode Adebimpe ◽

Adewale F. Lukman ◽

Olajumoke Oludoun ◽

Oluwakemi E. Abiodun

Keyword(s):

Regression Model ◽

Poisson Regression ◽

Generalized Linear Model ◽

Real Life ◽

Poisson Regression Model ◽

Likelihood Estimator ◽

Ridge Estimator ◽

Liu Estimator ◽

Life Study ◽

Ridge Regression Estimator

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 the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

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Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

F1000Research ◽

10.12688/f1000research.53987.2 ◽

2021 ◽

Vol 10 ◽

pp. 548

Author(s):

Benedicta B. Aladeitan ◽

Olukayode Adebimpe ◽

Adewale F. Lukman ◽

Olajumoke Oludoun ◽

Oluwakemi E. Abiodun

Keyword(s):

Regression Model ◽

Poisson Regression ◽

Generalized Linear Model ◽

Real Life ◽

Poisson Regression Model ◽

Likelihood Estimator ◽

Ridge Estimator ◽

Liu Estimator ◽

Life Study ◽

Ridge Regression Estimator

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 the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

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Preliminary test almost unbiased ridge estimator in a linear regression model with multivariate Student-t errors

Acta et Commentationes Universitatis Tartuensis de Mathematica ◽

10.12697/acutm.2011.15.03 ◽

2020 ◽

Vol 15 (1) ◽

pp. 27-43

Author(s):

Jianwen Xu ◽

Hu Yang

Keyword(s):

Regression Model ◽

Sufficient Conditions ◽

Preliminary Test ◽

Multiple Regression Model ◽

Regression Coefficients ◽

Lagrangian Multiplier ◽

Ridge Estimator ◽

Lm Tests ◽

Theoretical Results ◽

Almost Unbiased

In this paper, the preliminary test almost unbiased ridge estimators of the regression coefficients based on the conflicting Wald (W), Likelihood ratio (LR) and Lagrangian multiplier (LM) tests in a multiple regression model with multivariate Student-t errors are introduced when it is suspected that the regression coefficients may be restricted to a subspace. The bias and quadratic risks of the proposed estimators are derived and compared. Sufficient conditions on the departure parameter ∆ and the ridge parameter k are derived for the proposed estimators to be superior to the almost unbiased ridge estimator, restricted almost unbiased ridge estimator and preliminary test estimator. Furthermore, some graphical results are provided to illustrate theoretical results.

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A new modified ridge-type estimator for the beta regression model: simulation and application

AIMS Mathematics ◽

10.3934/math.2022062 ◽

2021 ◽

Vol 7 (1) ◽

pp. 1035-1057

Author(s):

Muhammad Nauman Akram ◽

◽

Muhammad Amin ◽

Ahmed Elhassanein ◽

Muhammad Aman Ullah ◽

...

Keyword(s):

Regression Model ◽

Mean Squared Error ◽

Model Simulation ◽

Beta Regression ◽

Explanatory Variables ◽

Squared Error ◽

The Matrix ◽

Biased Estimators ◽

Highly Correlated ◽

Beta Regression Model

<abstract> <p>The beta regression model has become a popular tool for assessing the relationships among chemical characteristics. In the BRM, when the explanatory variables are highly correlated, then the maximum likelihood estimator (MLE) does not provide reliable results. So, in this study, we propose a new modified beta ridge-type (MBRT) estimator for the BRM to reduce the effect of multicollinearity and improve the estimation. Initially, we show analytically that the new estimator outperforms the MLE as well as the other two well-known biased estimators i.e., beta ridge regression estimator (BRRE) and beta Liu estimator (BLE) using the matrix mean squared error (MMSE) and mean squared error (MSE) criteria. The performance of the MBRT estimator is assessed using a simulation study and an empirical application. Findings demonstrate that our proposed MBRT estimator outperforms the MLE, BRRE and BLE in fitting the BRM with correlated explanatory variables.</p> </abstract>

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