scholarly journals Preliminary-Test Estimation of the Error Variance in Linear Regression

1987 ◽  
Vol 3 (2) ◽  
pp. 299-304 ◽  
Author(s):  
Judith A. Clarke ◽  
David E. A. Giles ◽  
T. Dudley Wallace
Keyword(s):  
Linear Regression ◽  
Mean Squared Error ◽  
Preliminary Test ◽  
Error Variance ◽  
Error Component ◽  
Quadratic Loss ◽  
Finite Sample ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Preliminary Test Estimation

We derive exact finite-sample expressions for the biases and risks of several common pretest estimators of the scale parameter in the linear regression model. These estimators are associated with least squares, maximum likelihood and minimum mean squared error component estimators. Of these three criteria, the last is found to be superior (in terms of risk under quadratic loss) when pretesting in typical situations.

scholarly journals Risk Comparison of Improved Estimators in a Linear Regression Model with MultivariatetErrors under Balanced Loss Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guikai Hu ◽  
Qingguo Li ◽  
Shenghua Yu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Loss Function ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Balanced Loss Function ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Improved Estimators

Under a balanced loss function, we derive the explicit formulae of the risk of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the feasible minimum mean squared error (FMMSE) estimator, and the adjusted feasible minimum mean squared error (AFMMSE) estimator in a linear regression model with multivariateterrors. The results show that the PSR estimator dominates the SR estimator under the balanced loss and multivariateterrors. Also, our numerical results show that these estimators dominate the ordinary least squares (OLS) estimator when the weight of precision of estimation is larger than about half, and vice versa. Furthermore, the AFMMSE estimator dominates the PSR estimator in certain occasions.

scholarly journals PMSE PERFORMANCE OF THE BIASED ESTIMATORS IN A LINEAR REGRESSION MODEL WHEN RELEVANT REGRESSORS ARE OMITTED

2002 ◽  
Vol 18 (5) ◽  
pp. 1086-1098 ◽  
Author(s):  
Akio Namba
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Positive Part ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Explicit Formulae ◽  
Biased Estimators

In this paper, we consider a linear regression model when relevant regressors are omitted. We derive the explicit formulae for the predictive mean squared errors (PMSEs) of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the minimum mean squared error (MMSE) estimator, and the adjusted minimum mean squared error (AMMSE) estimator. It is shown analytically that the PSR estimator dominates the SR estimator in terms of PMSE even when there are omitted relevant regressors. Also, our numerical results show that the PSR estimator and the AMMSE estimator have much smaller PMSEs than the ordinary least squares estimator even when the relevant regressors are omitted.

scholarly journals Attack-resilient minimum mean-squared error estimation

2014 ◽  
Author(s):  
James Weimer ◽  
Nicola Bezzo ◽  
Miroslav Pajic ◽  
Oleg Sokolsky ◽  
Insup Lee
Keyword(s):  
Error Estimation ◽  
Mean Squared Error ◽  
Minimum Mean Squared Error ◽  
Squared Error
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