scholarly journals Two-Parameter Modified Ridge-Type M-Estimator for Linear Regression Model

2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Adewale F. Lukman ◽  
Kayode Ayinde ◽  
B. M. Golam Kibria ◽  
Segun L. Jegede
Keyword(s):  
Monte Carlo Simulation ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Linear Regression Analysis ◽  
Ordinary Least Squares ◽  
M Estimator ◽  
Ordinary Least Squares Estimator ◽  
General Linear Regression Model ◽  
Two Parameter

The general linear regression model has been one of the most frequently used models over the years, with the ordinary least squares estimator (OLS) used to estimate its parameter. The problems of the OLS estimator for linear regression analysis include that of multicollinearity and outliers, which lead to unfavourable results. This study proposed a two-parameter ridge-type modified M-estimator (RTMME) based on the M-estimator to deal with the combined problem resulting from multicollinearity and outliers. Through theoretical proofs, Monte Carlo simulation, and a numerical example, the proposed estimator outperforms the modified ridge-type estimator and some other considered existing estimators.

scholarly journals Use the method of parsing anomalous valueIn estimating the character parameter

2009 ◽  
Vol 15 (53) ◽  
pp. 1
Author(s):  
حازم منصور كوركيس
Keyword(s):  
Linear Regression ◽  
Singular Value Decomposition ◽  
Linear Regression Model ◽  
Ordinary Least Squares ◽  
Singular Value ◽  
Regression Estimator ◽  
Ordinary Least Squares Estimator ◽  
General Linear Regression Model ◽  
Ridge Regression Estimator ◽  
Value Decomposition

In this paper the method of singular value decomposition  is used to estimate the ridge parameter of ridge regression estimator which is an alternative to ordinary least squares estimator when the general linear regression model suffer from near multicollinearity.

scholarly journals Feasible Generalized Stein-Rule Restricted Ridge Regression Estimators

2017 ◽  
Vol 13 (1) ◽  
pp. 77-97
Author(s):  
Nimet Özbay ◽  
Issam Dawoud ◽  
Selahattin Kaçıranlar
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Simulation Experiment ◽  
Regression Estimators ◽  
Coefficient Vector ◽  
General Linear Regression Model

Abstract Several versions of the Stein-rule estimators of the coefficient vector in a linear regression model are proposed in the literature. In the present paper, we propose new feasible generalized Stein-rule restricted ridge regression estimators to examine multicollinearity and autocorrelation problems simultaneously for the general linear regression model, when certain additional exact restrictions are placed on these coefficients. Moreover, a Monte Carlo simulation experiment is performed to investigate the performance of the proposed estimator over the others.

scholarly journals A New Biased Estimator to Combat the Multicollinearity of the Gaussian Linear Regression Model

Stats ◽  
2020 ◽  
Vol 3 (4) ◽  
pp. 526-541
Author(s):  
Issam Dawoud ◽  
B. M. Golam Kibria
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Real Life ◽  
Multiple Linear Regression Model ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Linear Regression Models ◽  
Ordinary Least Squares Estimator

In a multiple linear regression model, the ordinary least squares estimator is inefficient when the multicollinearity problem exists. Many authors have proposed different estimators to overcome the multicollinearity problem for linear regression models. This paper introduces a new regression estimator, called the Dawoud–Kibria estimator, as an alternative to the ordinary least squares estimator. Theory and simulation results show that this estimator performs better than other regression estimators under some conditions, according to the mean squares error criterion. The real-life datasets are used to illustrate the findings of the paper.

A Mathematical Comparison of the Lachance - Traill Matrix Correction Procedure with Statistical Multiple Linear Regression Analysis in XRF Applications

1992 ◽  
Vol 36 ◽  
pp. 1-10
Author(s):  
Anthony J. Klimasara
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Linear Regression Analysis ◽  
Multiple Linear Regression Model ◽  
Mathematical Meaning ◽  
Matrix Correction ◽  
Independent Variables ◽  
Xrf Analysis

AbstractIt will be shown that the Lachance-Traill XRF matrix correction equations can be derived from the statistical multiple linear regression model. By selecting and properly transforming the independent variables and then applying the statistical multiple linear regression model, the following form of the matrix correction equation is obtained:Furthermore, it will be shown that the Lachance-Traill influence coefficients have a deeper mathematical meaning. They can be related to the multiple regression coefficients of the transformed system:Finally, it will be proposed that the Lachance-Traill model is equivalent to the statistical multiple linear regression model with the transformed independent variables. Knowing these facts will simplify correction subroutines in Quantitative/Empirical XRF Analysis programs. These mathematical facts have already been implemented and presented in a paper: “Automated Quantitative XRF Analysis Software in Quality Control Applications” (Pacific-International Congress on X-ray Analytical Methods, Hawaii, 1991).This demonstrates that the Lachance-Traill model has a strong mathematical foundation and is naturally justified mathematically.

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