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 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 A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications

Scientifica ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
B. M. Golam Kibria ◽  
Adewale F. Lukman
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Real Life ◽  
Economic Data ◽  
Nonlinear Regression Models ◽  
Shrinkage Methods ◽  
Regression Estimators ◽  
Better Than

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.

scholarly journals Performance of Some Stochastic Restricted Ridge Estimator in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jibo Wu ◽  
Chaolin Liu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Ridge Estimator ◽  
Numerical Example ◽  
Regression Estimators ◽  
Mixed Estimator

This paper considers several estimators for estimating the stochastic restricted ridge regression estimators. A simulation study has been conducted to compare the performance of the estimators. The result from the simulation study shows that stochastic restricted ridge regression estimators outperform mixed estimator. A numerical example has been also given to illustrate the performance of the estimators.

scholarly journals Modified One-Parameter Liu Estimator for the Linear Regression Model

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Adewale F. Lukman ◽  
B. M. Golam Kibria ◽  
Kayode Ayinde ◽  
Segun L. Jegede
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Real Life ◽  
Liu Estimator ◽  
Real Life Data ◽  
Squared Prediction Error ◽  
Simulation Results ◽  
Better Than

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 illustrate the findings of the paper and the performances of the estimators assessed by MSE and the mean squared prediction error. The application result agrees with the theoretical and simulation results.

Cadmium-hazard mapping using a general linear regression model (Irr-Cad) for rapid risk assessment

2008 ◽  
Vol 31 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Robert W. Simmons ◽  
Andrew D. Noble ◽  
P. Pongsakul ◽  
O. Sukreeyapongse ◽  
N. Chinabut
Keyword(s):  
Risk Assessment ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
General Linear ◽  
Hazard Mapping ◽  
General Linear Regression Model

scholarly journals The selective regularization of a linear regression model

2021 ◽  
Vol 2099 (1) ◽  
pp. 012024
Author(s):  
V N Lutay ◽  
N S Khusainov
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Triangular Decomposition ◽  
System Matrix ◽  
Original Dataset ◽  
The Matrix ◽  
Matrix Conditioning ◽  
Selection Of

Abstract This paper discusses constructing a linear regression model with regularization of the system matrix of normal equations. In contrast to the conventional ridge regression, where positive parameters are added to all diagonal terms of a matrix, in the method proposed only those matrix diagonal entries that correspond to the data with a high correlation are increased. This leads to a decrease in the matrix conditioning and, therefore, to a decrease in the corresponding coefficients of the regression equation. The selection of the entries to be increased is based on the triangular decomposition of the correlation matrix of the original dataset. The effectiveness of the method is tested on a known dataset, and it is performed not only with a ridge regression, but also with the results of applying the widespread algorithms LARS and Lasso.

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