Improper use of the ordinary least squares estimator in the switching regression model

1984 ◽  
Vol 13 (14) ◽  
pp. 1781-1791
Author(s):  
Kurt Brännäs ◽  
Stig Uhlin
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Switching Regression ◽  
Ordinary Least Squares Estimator ◽  
Improper Use

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.

ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS

2002 ◽  
Vol 18 (5) ◽  
pp. 1121-1138 ◽  
Author(s):  
DONG WAN SHIN ◽  
MAN SUK OH
Keyword(s):  
Least Squares ◽  
Asymptotic Efficiency ◽  
Characteristic Root ◽  
Sufficient Conditions ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Characteristic Roots ◽  
Generalized Least Squares Estimator ◽  
Ordinary Least Squares Estimator

For regression models with general unstable regressors having characteristic roots on the unit circle and general stationary errors independent of the regressors, sufficient conditions are investigated under which the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. A key condition for the asymptotic efficiency of the OLSE is that one multiplicity of a characteristic root of the regressor process is strictly greater than the multiplicities of the other roots. Under this condition, the covariance matrix Γ of the errors and the regressor matrix X are shown to satisfy a relationship (ΓX = XC + V for some matrix C) for V asymptotically dominated by X, which is analogous to the condition (ΓX = XC for some matrix C) for numerical equivalence of the OLSE and the GLSE.

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