scholarly journals A note on the correlation betweenS 2 and the least squares estimator in the linear regression model

1994 ◽  
Vol 35 (1) ◽  
pp. 42-42
Author(s):  
Henning Knautz ◽  
Götz Trenkler
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Least Squares Estimator

Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances

1997 ◽  
Vol 13 (3) ◽  
pp. 406-429 ◽  
Author(s):  
Anoop Chaturvedi ◽  
Hikaru Hasegawa ◽  
Ajit Chaturvedi ◽  
Govind Shukla
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Regression Coefficients ◽  
Confidence Sets ◽  
Generalized Least Squares Estimator ◽  
Coverage Probabilities

In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

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.

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